The same here - Android phone, Minecraft Bedrock 1.16.201 hotfix version. Reinstallation does not help. Everything works for me only the first run after the installation when a user must log-in first time. After this, everytime I run Minecraft it can't connect to Marketplace and user account is not loaded too.
It only shows last played character (I think it is cached, because it is old version now). Character modification does not work, it shows only non-marketplace items/parts. No Marketplace button animation, no user owned content, etc.
On Windows 10, everything work as expected. Literally, marketplace works, my owned content is here, game shows all my characters and they can be edited, char. editor shows all items, etc.
This issue is already created here: MCPE-113383