Builds on trevorgordon981's #50589 (cherry-picked as the previous commit).
The #50394 cooldown reset only ran inside the async _shutdown coroutine,
which is skipped on the empty-_servers fast path — the most common state
when a server failed to connect (failed servers are never recorded in
_servers). It was also skipped when the MCP loop wasn't running.
Clear _server_connect_retry_after/_server_connect_failures on the fast
path and in a final unconditional sweep so a full shutdown/restart always
re-attempts every configured server immediately. Adds regression tests
for both paths.
