Can you confirm whether this issue only occurs in a specific world, seed, or location?
If not — and it happens globally across different worlds and locations— this may be caused by Cinematic Camera mode being accidentally toggled on. Try hit F8 (default) to disable it.
If you want you can also unbind or change the key to prevent this from happening again.
My brain needed a moment to stop buffering after reading that
You are holding right-click to draw the bow.
While still holding right-click, you drop the bow via
Q
.You keep walking, and movement stays slow, even though the bow is no longer in their hand.
Just to confirm—remember, the bow is meant to be held, not put.