Right-clicking a tamed wolf/cat while it is riding an entity plays the hand animation

The Bug

When right-clicking a tamed wolf or cat while it is riding an entity such as a boat, minecart, or any other entity using the /ride command, the hand animation plays, but nothing visually occurs to the wolf/cat. Note that the wolf/cat has been sat down or stood up by the player, but this is not shown (until the player reloads the world; see MC-267827). This gives the impression of the player right-clicking the mob with no result, which can confuse the player.

This does not occur with tamed parrots.

How to Reproduce

1. Summon a wolf and tame it using bones. This can also be done with cats, tamed with raw cod or raw salmon.
2. Push the wolf/cat into a boat.
3. Right-click the wolf/cat while it is in the boat.
4. Note how the hand animation plays, despite the wolf/cat not visually doing anything different.

Additional Notes

Related to MC-114112 and MC-249424.