If Banned disable extension
Add a radio option to extension capabilities, so that if a member of chat is banned, like how chat gets a overlay saying you are banned.
An extension could have a twitch provided blocking overlay for a specific extension if the developer enables this as a option.
So if a member of chat is banned, the extension unloads
And if a chat banned member loads the page the extension doesn't even load and presents the is banned UI (omit the unban request button just overlay the extension)