The sun will move in a line very close to a line from due east to due west, directly overhead. It is "close to" not "exactly in".

The problem is the equinox is a moment in time it is not a day. If you look at https://en.wikipedia.org/wiki/Equinox you can see the time was in March 20 15:33 UTC and on September 23 is was 01:04 UTC, those time are rounded to minutes. The day of the equinox is the day it occurs not that is during the whole day.

So it is only one moment in time the equator is in line with the ecliptic.

If we assume the rate of change of axial tilt is constant we can calculate the cage during the day, I believe this is an approximation because of the elliptic orbit of Earth but it is a good enough approximation for my point.

The change in a year is 4 x 23.4 degrees = 93.6 degrees. Per day it is 93.6/365 =0.27 degrees. So on the day of the equnox the sun is up close to 12 hours and the equator change relative to the ecliptic is 0.27/2 =0.135 degrees.

So during the time the sun is up on the day of the equinox, the equator will change its tilt relative to the ecliptic by around 0.14 degrees. So even if the sunrise is exactly due west it will set a small bit off due west. The difference can be even higher because for half of the equator it will be night when the equinox occurs so will be off it even before the day start or before depending on you relative direction, let's double the error and ger a max error of around 0.3 degrees

So if due east and due west mean within 0.3 degrees then the sunrise and sunset direction are correct. If it is 0 error then it is only one spot on earth it is true for sunset and one for sunrise, the spots when the events are on the moment of the equinox.