docs(events): Phase 10 as built — the integrations, and a ceiling per firing

Five files. `EVENTS.md` §F gains "What Phase 10 settled" and §D/§J are corrected
to what was built; `EVENTS_PLAN.md` records the phase as built with its six
decisions, the live walk and the three defects it found; `MODULE_API.md` folds
two envelope members into 1.10.0 in place; `ENGAGEMENT.md` §8.5's "come back for
X" row is resolved; `BACKEND_DESIGN.md` gains the eleventh event table and the
two columns Phase 10 put on tables that already existed.

The four contract findings, three of which are rules rather than facts about
events:

- a firing may carry a ceiling of its own and it may only ever NARROW, applied
  at the send-time G24 gate as meet(declared, emitted). §I promised a rehearsal
  "ceilinged to staff" and nothing implemented it;
- two incomparable ceilings refuse rather than resolve, which is §5.1a rule 3
  reused rather than re-argued;
- a module reports participants on the success envelope and there is no other
  door;
- a trigger that is not also a STREAM has no push and says nothing about it, so
  every stream must be a trigger while a trigger need not be a stream.

And a trigger's `description` is read by a recipient, not only by an operator:
it is the structural projection's `intro` fallback, so a line naming its own
audience ends up in that audience's inbox.

- [x] AI-assisted: Claude Code (Opus 5).

Code: RunicGateway/website#TBD.

Co-Authored-By: Claude <noreply@anthropic.com>

🤖 Generated with [Claude Code](https://claude.com/claude-code)

website/ENGAGEMENT.md

@@ -4333,7 +4333,7 @@ worth confirming in Phase 4 rather than discovering in Phase 11.
 | **Welcome / first steps** after registration | `users.created_at` | ⚠ needs a time-based evaluator | email | delayed (e.g. +1 h) |
 | **Finish setting up** — no linked game account after N days | `shard_links` absence | ⚠ module-supplied predicate | email, in-app | delayed |
 | **We miss you** — no login in N days | `users.last_login_at` | ⚠ needs a scheduled sweep | email | monthly, hard cap |
-| **Come back for X** — a scheduled event is starting | operator-authored | ❌ needs a manual/scheduled trigger type | email, push, in-app | scheduled |
+| **Come back for X** — a scheduled event is starting | `event.run.started`, emitted by the event runner | ✅ **built — `EVENTS_PLAN.md` Phase 10**. It is a trigger AND a stream, which is what gives it push: the push channel is stream-keyed, so the six other `event.` triggers are email and in-app only | email, push, in-app | on the run |
 | **Your invite is about to expire** | `user_invites.expires_at` | ⚠ | email | delayed |
 | **Account dormant, scheduled for cleanup** | policy | ❌ no dormancy policy exists | email | scheduled, staged |