When using ^ to execute a command relative to where an arrow is facing, the axis rarely in the correct location. For example:
/execute as @e [type=arrow] at @s positioned ^ ^ ^3 run particle minecraft:electric_spark_particle
This should summon the particle 3 blocks in front of where the arrowhead is facing, this is not the case. Instead, the axes seem to start oriented relative to where the shooter is facing - but in a strange way. The ^z axis (stars particles) should always be tending forwards from the arrowhead, but this is not the case.
Here is a video showcasing the inconsistent axis orientations. I am also currently testing other projectiles.

https://www.youtube.com/watch?v=kStg77OEUFU&ab_channel=Misty