[Improve] Loosen the addressee gate for unmentioned replies and log its scores

[daniel-lxs]

What changed

• The unmentioned-reply gate routes when Roomote is the majority addressee (probability at least 0.5) instead of requiring 0.85. Human-to-human traffic scores far below this, and a majority bar holds up across judgment backends whose absolute probabilities are calibrated differently. Routing is still not a reply: Fast keeps its own rule to stay silent in a multi-human thread when Roomote was not the last speaker.
• The second question no longer asks whether the reply expects a response. It asks whether the reply is only a closing acknowledgement ("ok thanks", "got it", an emoji), and a reply is dropped only when that is more likely than not. Remarks, jokes, and short follow-up questions aimed at Roomote now route; sign-offs still do not.
• The model is consulted only when another human is part of the conversation: someone else has posted in the thread, somebody else was mentioned earlier, or the reply itself mentions somebody else. A sender alone with Roomote has only one possible addressee, so those replies route on the heuristic with no judgment call. Slack and Discord pass the reply's own peer-mention flag; Teams already refuses such replies before routing.
• Addressee probabilities must form a distribution (sum to one within a small tolerance) and the likeliest addressee is computed from them rather than read from the reported choice, so the lower bar cannot be satisfied by a malformed vector.
• Every decision logs its probabilities and outcome under [UnmentionedThreadReply], with the message id but never the text, so the gate can be tuned from ordinary logs.
• Docs on Slack, Discord, Teams, and personal settings describe the acknowledgement rule, with a changeset.

Why this change was made

In a real multi-person thread the gate stayed silent on "Which test?" asked right after a Roomote message and on a joke aimed at Roomote, which read as only answering explicit mentions. The 0.85 bar was set on one judgment backend and does not transfer to another.

Impact

• Deployments with a judgment backend route more unmentioned replies aimed at Roomote; peer discussion and acknowledgements stay silent. Deployments without one are unchanged.
• Evidence: 126 routing and judgment tests, API typecheck, formatting, and lint pass. A real 24-message multi-person thread replayed through the gate against Jev: every message aimed at Roomote routes (0.87 to 0.99), every human-to-human line stays below 0.45, and the only sign-off is caught as an acknowledgement at 0.94; one ambiguous line ("Can we get the scores?") routes at 0.56. Live on a local stack through the mock Slack harness: in a multi-person thread a remark aimed at Roomote routed and got a reply, a thanks stayed silent, and a message to a colleague stayed silent; in a thread with a single person, two unmentioned replies routed with no judgment call at all. The gate's own judgment call measured about 300 ms per message on Jev via OpenRouter. A who-spoke-last hint was tried and dropped: it pushed post-answer commentary between humans to 0.78. Teams has no harness and is covered by unit tests only.

[roomote-community]

No code issues found. See task

• apps/api/src/handlers/shared/unmentioned-thread-reply.ts:410 Majority gate routes a tied addressee distribution as Roomote.
• apps/api/src/handlers/shared/unmentioned-thread-reply.ts:415 Sum tolerance lets a non-majority Roomote score route.
• apps/api/src/handlers/shared/unmentioned-thread-reply.ts:431 Inclusive cutoff routes Roomote when it only ties the alternatives combined.

_{Reviewed 4c3bc98}