MatrixRTC: New membership manager

[toger5]

Fixes: https://github.com/element-hq/voip-internal/issues/309
Part of element-hq/element-call#2972.

This does not yet use the new manager by default. It only runs the test suite with it.

Notes on error cases encountered when making HTTP requests to the Homeserver:

Type	MatrixClient stack	RoomWidgetClient stack
"Local" request timeout enforced by the Matrix client	throws Error with name === AbortError	?
HTTP 5xx response from homeserver	throws HttpError	throws MatrixError
Network/socket error/timeout	throws ConnectionError	?
Request timeout between widget and host Matrix client	n/a	now mapped to ConnectionError as part of this PR

Checklist

• Tests written for new code (and old code if feasible).
• New or updated public/exported symbols have accurate TSDoc documentation.
• Linter and other CI checks pass.
• Sign-off given on the changes (see CONTRIBUTING.md).

[hughns]

I like the direction this is heading 👍

[hughns]

Latest changes look good

[dbkr]

Thanks for the changes: I think splitting up the handler function has made a big difference in particular. I think I'm happy to give this a go.

[hughns]

Awesome. It's great to get this over the line. 👍

[hughns]

@toger5 one more thing that could go in this PR, but could be a separate one, is adding some comments to say what is a workaround due to element-hq/synapse#17810 having not landed.

This would make it easier to come back and remove the workaround later.

[toger5]

@toger5 one more thing that could go in this PR, but could be a separate one, is adding some comments to say what is a workaround due to element-hq/synapse#17810 having not landed.

I will do this as a seperate PR.