Element-web: Community filter page/room list merger

[Fidgetcetera]

Is your suggestion related to a problem? Please describe.
The community pages are... a bit of a mess, and the filter buttons don't make sense, and actually viewing a community's description, especially if there are rules or other important info, is hard to even realize how to reach. Filtering the rooms you're in, and the DMs you have with people in the community, is neat but feels... incomplete.

Describe the solution you'd like
I'm thinking about a sort of merger between the room list of communites' description pages, and the room list of filtering, as well as a few tweaks to the filter page to make it stand out.

1. Most importantly: When you filter by rooms in the community, give a big, clear button with the community avatar as the icon, that lets you view the community's long description and user list. (The room list in the longdesc view should be relatively less necessary given the next bit.)
2. Add a hidable section under "rooms" (which could be "community rooms") that is "unjoined rooms", which lists any publicly joinable rooms in the community.
3. Move "people" below one or both of those, or allow people to move around the "rooms" and "people" lists so that they can prioritize as they like.
4. Also probably show "people" as "people in community", for extra clarity.

Describe alternatives you've considered
There's a lot of ways you could take this - minor and major tweaks. You could even make the opposite suggestion to what we did, and remove filtering in favor of just the community description/room list page? It's a bit hard to think of any one specific alternative design here, though.

Additional context
If I get the spoons, I'd try to mock this up, especially if someone isn't sure what this design would look like, but I extremely cannot guarantee anything.

[NoraCodes]

This feature, or something like it, is a pretty big deal for me. I really want my Matrix community to replace my Discord server, which as of now has 18 users and 36 channels. It's the system of record for our personal plans, activism, and art that we share with each other.

Matrix has most of the features we need to make this transition, plus a few extras, and federation is nice. However, the communities UI is so confusing and fundamentally lacking that the people I've tried to move over have bailed almost immediately. I think this design is a good one and is likely to make Discord transplants much more comfortable.