docs: threads + July batch across catalog/README/TODO/BUGS

- LOTUS_FEATURES: new Threads section (+TOC) — panel, summary chips, thread
  composer isolation, under-the-hood notes; entries for KaTeX math, opt-in
  encrypted-search cache, hardened session storage, Crypto Diagnostics.
- README: threads bullet (with the replies-move-to-panel release note), math,
  search-cache bullets.
- LOTUS_TODO: P3-8 → [~] implemented + 6-step live-QA checklist; P4-1 marked
  unblocked.
- LOTUS_BUGS: Needs Verification rows for P3-8 / P4-4 / P4-8 / session sync.

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

README.md

@@ -18,6 +18,7 @@ The Lotus Chat logo (`public/res/Lotus.png`) is a derivative work based on the o
 
 ### Messaging
 
+- Threads: reply in a thread and read/write the whole conversation in a side panel — root messages show a "N replies" chip with an unread badge (threaded replies live in the panel now, not inline in the room)
 - See who has read each message, and track delivery status (sending / sent / failed)
 - Bookmark any message and revisit saved messages from the sidebar
 - Schedule messages to send at a specific time
@@ -33,6 +34,8 @@ The Lotus Chat logo (`public/res/Lotus.png`) is a derivative work based on the o
 - Search for and send GIFs from a built-in GIF picker
 - Control voice message playback speed: 0.75× / 1× / 1.5× / 2×
 - Search messages with a date range filter
+- Optional persistent search index for encrypted rooms (off by default — stores decrypted text on your device; clearable, wiped on logout)
+- Write math with LaTeX: `$inline$` and `$$block$$` render via KaTeX (spec `data-mx-maths` supported)
 - Room topics support rich formatting (bold, links, italics)
 - Deleted messages show a placeholder instead of disappearing
 - Code blocks highlight syntax for JS/TS, Python, and Rust