This coding bug has not been a new problem, it has existed for several versions before 1.16.0
The effects vary, and include: all custom skins fail to transfer to other devices playing peer to peer and everyone appears as Steve or Alex to everyone, skins can swap between players, players who join can end up with someone else's skin. On client side, everything appears normal, and if a players views their avatar in third person, a player will see their custom skin, pointing to a problem with the coding allowing peer to peer among devices.

I find it disturbing that this bug has gone unreported or unresolved for several versions.

Nicolaus Alexander Eckelman Clement