docs: Slack-style per-thread notifications (P4-1) across catalog/README/TODO/BUGS

LOTUS_FEATURES: Notifications subsection under Threads (participating default,
per-thread All/Mentions/Mute, badge behavior). README: thread-notifications
bullet. LOTUS_TODO: P4-1 → [~] + 6-step live-QA checklist + caveats.
LOTUS_BUGS: verification row.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

LOTUS_BUGS.md

@@ -36,6 +36,7 @@ Implemented and gate-green; confirm each per `LOTUS_TESTING.md`, then delete the
 | P4-4 | KaTeX math (`$…$`, `$$…$$`, data-mx-maths; lazy chunk)                                | `utils/mathParse.ts`, `components/math/`             | send `$x^2$`, `$$\int f$$`, `$5 and $10` (stays text), math inside code block (stays text) |
 | P4-8 | Encrypted-search cache (opt-in toggle, clear button, logout wipe)                      | `utils/searchCache.ts`, message-search               | enable in search panel → search → reload → coverage persists; logout wipes        |
 | N97a | Session blob migration + cross-tab logout sync                                        | `state/sessions.ts`, `useSessionSync`                | login on old build → new build migrates; logout in tab A → tab B drops to auth    |
+| P4-1 | Slack-style thread notifications (participating default, All/Mentions/Mute, badge math) | `utils/threadNotifications.ts`, `ClientNonUIFeatures`, `roomToUnread` | 6-step checklist in LOTUS_TODO §P4-1                                              |
 
 **Verified working in live testing (2026-06):** A2, B1–B4, C1, C3, D (mic/camera/deafen/screenshare/fullscreen/more-menu/PiP). Denoise quality in D is still poor — tracked under the denoise project, not a regression.