Follow-up to #59195. While verifying that fix against prod we hit a log
that couldn't distinguish "retrying with a fresh token that is still
revoked" from "silently retrying with the same dead token because the
server returned no connection info" (e.g. a collab deploy predating
#59195). Make the retry loop self-diagnosing:

- Warn when `RejoinRoomResponse` carries no `live_kit_connection_info`,
since the loop then reuses the existing token.
- On refresh, log whether the token actually changed.

Release Notes:

- N/A

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Co-authored-by: Claude Fable 5 <noreply@anthropic.com>