Rabbits spawned by players in spectator mode do not naturally pathfind. Other entities such as sheep will continue to move around but rabbits will stare off into the distance unable to do anything. The rabbit will run away from monsters such as zombies though once they have finished fleeing from the zombie they will again become frozen.
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I can confirm, if you spawn them while in spectator it's easier
This is also the case with squids.
Can confirm in 20w51a.
It's intended that random wandering only occurs when a non-spectator is nearby; see MC-47533. It's easy to verify that the rabbits start moving again once you switch to Survival/Creative.
Unable to reproduce. Please include a video or screenshot with the F3 debug screen enabeled