Move the location where we send the "close thread" message so it will
always happen when we're waiting on the thread to join. Also stop
blocking forever on queues, but spin the loop every second to check if
the connection closed flag got set.

Differential Revision: https://phabricator.services.mozilla.com/D111323

bugzilla-url: https://bugzilla.mozilla.org/show_bug.cgi?id=1703921
gecko-commit: f22a4ed1ed22fe69008fc1036c81baec9e1c4527
gecko-reviewers: twisniewski