First, some terms. There is "true north" and "magnetic north." True north is perpendicular to east. Magnetic north is close to perpendicular to east, but not quite.

True north is defined as the point that Earth's rotation axis points through. To visualize, look at this globe. The "true north" pole is where the pole sticks through the globe, the place the Earth is rotating about. This is what is perpendicular to east. Which, when you think about it as a rotation, makes sense. As the Earth rotates, the Sun is going to appear to rise in the direction the Earth is spinning. This globe photo may help illustrate that if it's not clear as of why.

Now, magnetic north is based on the magnetic field of the Earth, and it is close to truth north, but the true north pole is about 1200 miles away from the magnetic north pole. In the latitude bands most people live in, that distance doesn't matter much- if you point true north of magnetic north, you're basically pointing in the same direction- but as you move really far north (or really far south), that distance matters more.

So, is it a coincidence that magnetic north and true north are close to aligned? No, it's also due to rotation. The Earth's magnetic field is caused by spinning liquid metal in the outer core, and that core's direction of spin is highly influenced by the direction of the Earth's rotation. So, most of the the time, the Earth's magnetic field is close to aligned with the Earth's rotation axis. Since the Earth's magnetic North pole was discovered, it has moved by 600 miles. The Earth's magnetic field will also flip-flop at some point in the future (Magnetic north pole will go to the geographic south pole) and has flip-flopped in the past. During this flip-flopping time, the magnetic north pole will have to wander all the way down the globe, and thus magnetic north and true north will be no where close to each other (and at some point, magnetic north will lie due east!). But most of the time, the Earth's magnetic field stays relatively aligned to the Earth's rotation.

(This is sort of going down a rabbit hole, but you can watch this video about why Canada labels their runways using true north, while most of the rest of the world uses magnetic north, but it comes down to how those little variations in where magnetic north is don't impact much, unless you're really far north or south)

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To add an extra level to the rabbit hole, there are actually three norths. True north, magnetic dip north, and geomagnetic north. True north has been covered, but magnetic dip north is the location where the magnetic field is oriented vertically (so if you had a magnetic inclinometer, where it would point vertically) whereas geomagnetic north is the intersection of the surface of the Earth with the best fit dipole field. In detail, if the Earth's magnetic field was a true dipole (like a bar magnet) then the north and south dip poles (1) would be antipodal with respect to each other and (2) they would be equivalent to the geomagnetic poles (which are by definition antipodal), but neither of those tend to be true as the location of the dip poles migrate as part of secular variation.

/u/Weed_O_Whirler has covered the relationship between the cardinal directions and the magnetic field of the Earth, but another aspect of your question is basically asking why do we use a coordinate system that (when viewed on a projected map) is a Cartesian coordinate system. At the simplest level, to define a location in an x-y plane, you need two coordinates. You could theoretically define two coordinate axes which are not at right angles to each other, but it would make defining coordinates way more complicated. The simplest solution is to have two orthogonal coordinate axes (and in reality, to have three orthogonal coordinate axes, i.e., elevation) to uniquely define locations. The same logic can be applied to spherical coordinate systems, i.e., why do we define locations with respect to intersections of sets of orthogonal planes with a sphere? Cause it's easier than defining coordinates with a non-orthogonal set of planes and their intersections with a sphere.

It's also worth noting that in most locations, it's actually rare that the sun rises/sets truly due east/west with respect to true north (and the location where the sun set/rises moves because of the inclination of the rotational axis with respect to Earth's orbital plane). Thus, east and west are not defined as such because of the sun, but rather because they specifically are directions along the equator which is orthogonal to the rotational axis. Even if we were on a planet that had a very high inclination (i.e., the orientation of the rotational axis was much closer to being parallel with the orbital plane) it would still make the most sense to define a set of coordinate axes that parallel the equator (and thus are perpendicular to the coordinate axis that parallels the rotational axis).

Getting back to the relation between our coordinate axes and the magnetic field, it would be interesting to consider a hypothetical of early navigation developing on a planet that had a setup like Uranus, which has a rotational axis nearly parallel to the orbital plane but also a magnetic field that is oriented at a high angle with respect to the rotational axis. We define coordinates on Uranus like we do on Earth, i.e., with respect to the rotational axis, but it's hard to know what kind of coordinate system one would develop if you were living on (a habitable rocky planet) that had a similar setup.

> magnetic dip north is the location where the magnetic field is oriented vertically

Presumably in general magnetic dip poles do not strictly need to some as a single pair and could come in any number of pairs? I am essentially thinking along the lines that there is no strict mechanism to enforce that only two such locations would exist in a general astrophysical dynamo (for example there are many locations with locally vertical field at the surface of the Sun).

I would assume so, but as far as I know on Earth, we tend to find two distinct dip poles roughly equivalent to a north and south pole (i.e., one with a +90 inclination and one with a -90 inclination). You might expect that during a geomagnetic reversal (which is often described as a weakening/temporary collapse of the dipole component and thus a relative strengthening of the higher order field components) you could have more than one pair of dip poles, maybe?

One thing I would like to add, the ☀️ sun moves along the ecliptic plane which changes depending on the time of year.

The ecliptic plane is defined as the imaginary plane containing the Earth's orbit around the sun. In the course of a year, the sun's apparent path through the sky lies in this plane. The planetary bodies of our solar system all tend to lie near this plane, since they were formed from the sun's spinning, flattened, proto-planetary disk.

The sun never truly "rises" in the East nor sets in the West.

https://www.nasa.gov/multimedia/imagegallery/image_feature_635.html

I remember seeing a documentary about Indonesian navigators, they do use the rising stars as their point of reference while we use the polar star. Also I read about the temple in Jerusalem and the Tabernacle) having had the door to the east for the same reason. So your scenario isn't that hypothetical, it did (and probably does) have real life application even on earth; using "north" or magnetism is just one of the possible and valid choices for describing directions that were used.

TL;DR: If you are interested, you'll be able to find examples on earth other than "magnetic north is up".

it's simply because the earth is a sphere that's spinning

considering a spinning sphere, then there's an axis; that's your north-south direction. and then perpendicular to that are planes within which things are spinning -- if you're somewhere on the surface of the earth you're moving in a circle -- that's your east-west direction

note that the notion of north etc is completely unrelated to the sun, it only has to do with the earth's rotation

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If you think that's strange, you should visit the South Pole. The sun travels in a circle, at an angle of elevation that slowly changes over the weeks and months. And the architects of the base have imposed a NSEW Cartesian grid over the area to make navigation and planning easier.

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It's best to describe a space using perpendicular axis, though not required. Strictly speaking you could have a coordinate system which doesn't have perpendicular axis, but the maths gets more complicated.

Mathematically speaking this is asking what the optimum choice of basis is for a space, a 2-d manifold in the case of the earth. So it's mostly just convention, to make the mathematics easier.

It's been about a decade since I touched linear algebra, so I'm sure someone more recent can expand on my answer, but that's the basic jist.

Because of the tilted axis of the earth, the sun only rises due east, and sets due west, at the spring and autumn equinoxes (around 21st March and 21st September).

The deviation from due-east / due-west at other times of the year is least near the equator and "beyond extreme" ;-) when you go beyond the arctic or antarctic circles.

https://www.timeanddate.com/astronomy/uk
Will show you lots of interesting information about the time of sunrise and sunset, and what azimuth the sun rises or sets at, for different places at different times of the year.
The link above takes you to a UK page, but you can set it to any country.

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Never? I'm pretty sure maths says it does it exactly twice per year, with the rise and set happenning at the same moment, at two specific points on opposite sides of the planet.

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Worth emphasizing your second paragraph: East and West are not defined by the sun rising and setting. That would be a very silly idea. They're perpendicular to North and South because they're defined as perpendicular to North and South.

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In linear algebra and other types of mathematics, the notion of perpendicular is generalized to "orthogonal" in different coordinate systems, with the idea that a certain type of "product" between two vectors (i.e. the "dot product" in our familiar cartesian coordinates, and more generally the "inner product") equals 0.

At a small enough scale we can treat the earth's surface as a flat plane and still get reasonable results, though on bigger scales we have to use a roughly spherical geometry. On a sphere you can still have two orthogonal axes for your coordinate system, just the path you travel affects what direction you end up facing differently from a plane. Triangles add up their angles differently from a flat plane, etc., but that only matters if you are traveling very far.

So there is one broader mathematical definition of perpendicular of which our coordinates on Earth are a special case. But why have we chosen perpendicular axes? Historically, perhaps because it's a simple and intuitive way of describing the geometry we can see and interact with. Sort of an emergent property of human thinking, when people in antiquity were working mathematics as it related to everyday experience. Humans seem to like symmetry and simplicity, so a four-fold symmetry of right angles is a "nice" coordinate system to us.

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