The Bug:

In Java edition, Allays have a rapid fluttering animation when moving quickly, like to an item/player/noteblock, as can be seen here:

In Bedrock however, they lack this animation when moving very quickly:

And there's actually an interesting reason as to why it's like this...

Origin and history of this bug:

Originally in Java, allays had no special wing movement animation. It was one speed and that was it, unlike Bedrock, which has two movement speeds; idle (slow) and moving (medium). This was part of a bug (MC-251518) that was fixed in Java in 22w24a, however the bug had to be reopened as Allays from Java still lacked the higher fidelity animations for their Idle, Movement, and Dancing Allays have on Bedrock.

During this fix however, Java Allays not only got a slow and medium wing movement speed, but also got an additional rapid movement speed when the Allays move especially fast, like when flying to an item, player, or noteblock.

So it went from Java having one and Bedrock having two animations, to Java having three and Bedrock still having two.