Trigonometry

https://youtu.be/RtnnEnUJPu0

Speed square has a "pivot" edge you can use that will show you the degree of cut you need to make.

There are a few ways you can go about it:

If you have a scrap piece of wood, you can cut it at an angle that you know is too wide and make small adjustments until it fits well in that lower corner.

You can make a few measurements to find the sides of the triangle that would form from conecting the top stair corner to the pillar and use that to calculate the lower corner angle.

You can use a speed square to get a fairly good approximation.

You can hold the handrail next to the gap at the appropriate heights and mark it with a pencil against the walls and like up the blade with the pencil marks.

However you approach it, don't worry too much about getting it perfectly flush with the walls. It is very likely that they are not flat (highly improbable that they are flat), and even a millimeter difference in position will visible change how it sits.

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The easiest way for you to approximate this would be to get a piece of scrap cut at 37degrees on one end and rest it on the cap wall and slide it up next to the post or wall and then make a scribe.

Almost all stair cases fall in the 36-39 degree range.

Cut your rail long and sneak it in. You’ll have to make adjustment cuts on the post and wall. It’s not uncommon for to have to cut a 37 at the post and a 38 with a 1 degree adjustment at the wall because of how out of plumb/square the framing is.

I've got one of those 12" angle finders for cutting trim - I've done stuff like this with it, like measure at each end for the height of the rail, and run a string or tack up a straight scrap of wood. Find the angle for each end. For something short like this, I might first cut from plywood or a 2x4 to make a template, cut a little fat and shave it bit by bit on the chop saw til it's a perfect fit, then transfer to your actual lumber. Many ways to skin a cat, I'm not a pro but I really enjoy designing and installing trim; windows and doors are more my thing though.

If you have a (pretty standard) carpenter's square, there are degree measurements on it. If you place the square against the railing, then hand a weighted string from the pivot location (all the angles will pint to it), it will tell you the angle of the railing.

Match that value on your miter box.

Don’t even need to approximate. Hold a scrap or your rail cut to rough length on the top of the skirt board and against the post and wall. Mark the angles using the wall and post as the straight edges. If everything’s plumb, you’ll cut both at the same angle.

Clamp it so it lines up with the bottom flush with the cap on the angled knee wall and then scribe your lines… I install handrails. That is how you do it. (most quickly and accurately anyway). Then you cut one side. Move your clamps up to where your handrail is going to be placed and check to see if the other line you haven’t cut yet is where it needs to be…(your wall and that post might not be plumb or there might be some wowing going on).

Eyeball it to make sure the second cut is where it should be. The angle should be the same as your first cut (maybe a bit more or less but if everything is plumb then it will be the same). Then put your piece of wood up and mark for spindles… if there is a slight (like really small) gap between your cuts and the wall and post, when you attach it it should suck in and get pretty tight.. just use some wood filler if there are noticeable gaps.

I’m guessing both the post and wall have good attachment points (solid framing timber beneath drywall) if not then attach it to whatever has the most solid attachment point first and the weakest last.