Add embeddable view of rooms for people to put on their own websites

As [mentioned by @marclaporte](https://matrix.to/#/!OvgDmYaPOFRRWnIdQe:half-shot.uk/$xRTuCoqAE1FaPolmO7RV381_f8OTFbXEA2F-b7hGOLg?via=half-shot.uk&via=matrix.org&via=gitter.im), it would be nice to have something comparable to [Gitter Sidecar](https://sidecar.gitter.im/) for embedding a chat room on your own website.

One option would be embedding the room view from this project (Matrix Public Archive). That would show the latest messages in the room and just direct you to a Matrix client to chat. I've also considered this option for replacing the featured communities on the Gitter homepage.

Perhaps served at a URL like: `/archives/r/matrixhq:matrix.org/${year}/${month}/${day}/~embed`

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https://github.com/vector-im/chatterbox also exists (https://element.io/blog/element-launches-chatterbox/) but is more for one-on-one chat with a support agent style of a thing at the moment. This would need to be extended/modified to support the Gitter Sidecar use case.

No files, tests, or entry points are named. Start by reviewing the existing room archive view and the proposed `/archives/r/matrixhq:matrix.org/${year}/${month}/${day}/~embed` route; done means an embeddable room view shows recent messages and directs visitors to a Matrix client for chatting.

Written by the indexing model from the issue text.