Purging a room can lead to stuck invites

This issue has been migrated from [#15085](https://github.com/matrix-org/synapse/issues/15085).

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The [Delete room API](https://matrix-org.github.io/synapse/latest/admin_api/rooms.html#delete-room-api) will kick out any existing *joined* members of the room, but does not (afaict) consider *invited* members.

Anyone with a pending invite then gets a stuck invite, because we are unable to generate a leave event.

Start with the Delete room API behavior described in the issue and trace how joined members are removed during room purging. Determine how pending invites should be handled so they no longer become stuck, then verify that purging a room leaves no unresolved invites.

Written by the indexing model from the issue text.