Invite only badge on room avatars

### Your use case

Currently Element-Web/Desktop shows a globe badge 🌐 for public rooms, so that you can immediately tell that what your are writing in the room is accessible by the public.

I would like to propose to add badges to also indicate whether a room is invite only (lock badge 🔒️) or accessible for space members (no badge or a shield 🛡️).

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

Start by locating the room avatar badge implementation in Element-Web/Desktop and reviewing how the existing public-room globe badge is determined. Define the invite-only and space-member states and confirm the badge treatment with the project before implementing; done means avatars clearly distinguish public, invite-only, and space-member rooms.

Written by the indexing model from the issue text.