When changing a wither's NoAI tag from 0, to 1, the wither will continue to track the last aggroed mob/player even though it has NoAI.
Damaging the Wither in the NoAI state also causes his rotation to change.
These changes are not visible on F3+B but can be visuallized via commands like:
/execute as @e[type=minecraft:wither,limit=1] at @s run particle minecraft:electric_spark ^ ^ ^5
This behavior is not shared with other mobs, which do not undergo rotation changes while NoAI is set to 1
Video proof: