The bug

Arrows without any motion ignore the rotation parameter of the /tp command and always try to match rotation [0, 0].
Arrows with motion always point in the direction they are moving towards, but that is likely working as intended.

How to reproduce

/summon minecraft:arrow ~ ~ ~ {NoGravity: 1}
/execute as @e[type=minecraft:arrow] at @s run tp @s ~ ~ ~ ~45 ~

→ The arrow is not going to rotate by 45 degree. It instead just face the original direction.