If you sprint while going forward and with a certain horizontal angle which has to be, according to my experimentations, between 1.9 and 3.9 or between -1.9 and -3.9 degrees off of one of the 4 directions (south, east, north, west), you are slightly pushed to the left or the right, depending on which of the 8 possible configurations you're replicating.

Details :

angle 2.5 -> pushed to the right

angle 87.5 -> pushed to the left

angle 92.5 -> pushed to the right

angle 177.5 -> pushed to the left

angle -177.5 -> pushed to the right

angle -92.5 -> pushed to the left

angle -87.5 -> pushed to the right

angle -2.5 -> pushed to the left

Also it looks like the more your angle is near 3.9 degrees off of one of the four directions, the more you'll be pushed.

Video showing the bug : https://www.youtube.com/watch?v=SApAawx6fGw

This video was not recorded in vanilla Minecraft but I tested it in vanilla and it happens too.

The bug didn't seem to work in 1.8.9 but it did in 1.16.4 and 1.17.1.