fix(terminal): report a click to the CLI only when it asked for the mouse

Found while verifying Auto Copy in a browser: a plain left click in a
claude/codex/gemini pane sent a synthetic SGR mouse report into the PTY
whether or not the program in that pane had ever enabled mouse tracking.
When the pane holds a plain shell (the CLI exited, or a shell was started
inside a session of that mode) readline prints the report as literal text
and it garbles the next line typed:

    $ [<0;88;20Mecho hello
    bash: 0: No such file or directory

The cause is that the browser could not know. The full strip
(isAltScreenStripMode) removes the mouse DECSETs from the stream, so
xterm's modes.mouseTrackingMode is permanently 'none' for those modes and
_sendSyntheticSgrTap() hand-encodes reports to stand in for xterm's own
encoder. With no state to consult it had to do that on every click.

What the strip removes, the server now remembers.
_recordStrippedMouseMode() records each sequence as it is stripped,
toState() publishes it as cliMouseTracking, and the browser's
_shouldReportMouseToCli() (renamed from _sessionUsesServerMouseStrip)
requires it at all three report sites: the desktop click, the touchend
tap, and the mobile tap classifier.

Details that are easy to get wrong:

* Only the tracking modes count (1000/1001/1002/1003). 1005/1006 select
  an encoding and 1007 is alt-scroll; a CLI that picks SGR encoding
  without turning tracking on is not asking about clicks, and counting
  those would put the stray reports straight back.
* Modes are held in a Set, so a TUI disabling a mode it never enabled
  cannot clear the ones that are really on.
* The change broadcasts immediately instead of through
  broadcastSessionStateDebounced: the flag flips when a dialog opens, and
  the user can click that dialog well inside the 500ms debounce window.
* It fails toward silence. After a server restart the flag is false until
  the CLI re-emits its DECSET, which tmux does at client attach.

Verified against a live claude 2.x session: the CLI holds a tracking mode
on continuously, so its clicks are still reported byte for byte as
before, while a bash prompt in the same stripped mode now reports
nothing and types cleanly. The flag also propagates live over SSE in both
directions, checked by toggling ?1002h/?1002l from inside the pane.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

docs/architecture-invariants.md

@@ -96,7 +96,9 @@ Implementation detail extracted from `CLAUDE.md` so that file stays small enough
 
 ### Terminal scrollback: strip flavors and wheel/touch forwarding
 
-**Two strip flavors, one carry** (#205, `session.ts:_handleTerminalOutput`): the FULL strip (`isAltScreenStripMode` = codex/claude/gemini) removes alt-screen toggles, `3J`, and mouse-tracking DECSETs. Every other mode (shell/opencode/antigravity/pi) gets the NARROW strip (`isMuxAltScreenOnlyStripMode`) — alt-screen toggles ONLY — and only when tmux-backed (`useMux`). Rationale: the tmux CLIENT emits `smcup` as its first bytes at attach, before any program runs, parking xterm in the scrollback-less alternate buffer for the whole session (touch scrolling no-ops; xterm's own wheel handler converts the wheel to Up/Down arrows = readline history cycling — both #205 symptoms). tmux never forwards a pane program's alt-screen toggles to its client (it repaints instead; measured — vim/less inside a pane emit zero to the client), so the only thing the narrow strip ever removes is tmux's own smcup. It keeps `3J` (a user's `clear` is a deliberate scrollback wipe) and the mouse DECSETs (tmux passes those through even with `mouse off`; stripping them would break htop/vim mouse support). ⚠️ The `useMux` gate is load-bearing: `startShell()`/`startInteractive()` fall back to a DIRECT PTY when mux creation fails, and there the inner program's own `?1049h` really does reach xterm — stripping it would break vim/less/htop for real. The replay path (`session-routes.ts`, via `session.usesMux`) applies the same narrow branch; the frontend `_sessionUsesServerMouseStrip()` mirror stays claude/codex/gemini because only the FULL strip touches mouse DECSETs. The chunk-boundary carry (`_altScreenSeqCarry`) runs for both flavors. Tests: `test/claude-scrollback-strip.test.ts`.
+**Two strip flavors, one carry** (#205, `session.ts:_handleTerminalOutput`): the FULL strip (`isAltScreenStripMode` = codex/claude/gemini) removes alt-screen toggles, `3J`, and mouse-tracking DECSETs. Every other mode (shell/opencode/antigravity/pi) gets the NARROW strip (`isMuxAltScreenOnlyStripMode`) — alt-screen toggles ONLY — and only when tmux-backed (`useMux`). Rationale: the tmux CLIENT emits `smcup` as its first bytes at attach, before any program runs, parking xterm in the scrollback-less alternate buffer for the whole session (touch scrolling no-ops; xterm's own wheel handler converts the wheel to Up/Down arrows = readline history cycling — both #205 symptoms). tmux never forwards a pane program's alt-screen toggles to its client (it repaints instead; measured — vim/less inside a pane emit zero to the client), so the only thing the narrow strip ever removes is tmux's own smcup. It keeps `3J` (a user's `clear` is a deliberate scrollback wipe) and the mouse DECSETs (tmux passes those through even with `mouse off`; stripping them would break htop/vim mouse support). ⚠️ The `useMux` gate is load-bearing: `startShell()`/`startInteractive()` fall back to a DIRECT PTY when mux creation fails, and there the inner program's own `?1049h` really does reach xterm — stripping it would break vim/less/htop for real. The replay path (`session-routes.ts`, via `session.usesMux`) applies the same narrow branch; the frontend mirror (`_shouldReportMouseToCli()`) stays claude/codex/gemini because only the FULL strip touches mouse DECSETs. The chunk-boundary carry (`_altScreenSeqCarry`) runs for both flavors. Tests: `test/claude-scrollback-strip.test.ts`.
+
+⚠️ **What the full strip removes, it must REMEMBER.** Stripping the mouse DECSETs means xterm's `modes.mouseTrackingMode` is permanently `'none'` for those modes, so the browser hand-encodes click reports to compensate (`_sendSyntheticSgrTap`). With no state to consult it did that on EVERY click, which delivered mouse reports to programs that never asked for them: the same pane runs a plain shell whenever the CLI has exited or a `shell` was started inside a claude-mode session, and a shell prints the report as literal text (`[<0;88;20M`), garbling the next line typed. `_recordStrippedMouseMode()` therefore records each stripped sequence as it goes and publishes `cliMouseTracking` through `toState()`, and `_shouldReportMouseToCli()` requires it. ⚠️ Only the TRACKING modes count (1000/1001/1002/1003): 1005/1006 select an ENCODING and 1007 is alt-scroll, and counting those would put the stray reports straight back. ⚠️ The change broadcasts IMMEDIATELY rather than through `broadcastSessionStateDebounced`, because the flag flips when a dialog opens and the user can click that dialog inside the 500ms debounce window. Measured on a live claude 2.x: the CLI holds a tracking mode on continuously (so clicks keep being reported exactly as before), while a bash prompt in the same stripped mode reports nothing. Fails toward silence: after a server restart the flag is false until the CLI re-emits, which tmux does at client attach.
 
 **Only claude ≥ 2.1.187 forwards the wheel; every other mode scrolls local scrollback** (#227 follow-up, `terminal-ui.js:_shouldForwardWheelToApp`). Codex was in the forward list until a reporter hit a completely dead wheel in codex tabs while the scrollbar drag worked. Measured against codex-cli 0.147.0 in a bare tmux: it never enables mouse tracking (`mouse_any_flag=0`) and SGR wheel reports fed to its PTY change nothing on screen, because it runs an INLINE viewport (`alternate_on=0`) and pushes its transcript into the terminal's own scrollback (tmux `history_size` grows) instead of paging in-app. So for codex, local scrollback IS the transcript and forwarding swallowed every tick. ⚠️ "The TUI is a strip mode" is NOT evidence that it consumes wheel reports — verify with a real `\x1b[<64;c;rM` write into a live pane before adding a mode here. Hand-encoded SGR TAPS stay enabled for codex (`_sessionUsesServerMouseStrip`); measured, they are no-ops that insert nothing, so click-to-position is simply unavailable there rather than harmful.