feat(approvals): let a watching session keep quiet, and fix the tui gate

The badge alone left the row in NEEDS YOU, which is the thing the issue was
about. The fix is the alert that does not fire.

An idle prompt from a session that is watching its own background work now
opens ALREADY acknowledged. `hook-event-routes` passes `Session.watching` to
`notePrompt()`, which sets `acknowledgedAt` and records why in a new
`acknowledgedReason`. Nothing new suppresses anything: `acknowledge()` has
always meant "the alert this prompt armed is spent", and the prompt itself
stays pending, answerable and available as Read My Mind context. A wrong label
therefore costs a card that does not blink, never an alert that was never
created.

Every surface follows from that. The broadcast carries the reason, so a live
page declines to arm the tab alert and raises no desktop notification. The push
is skipped, since a false alarm is hardest to ignore on a phone. A reloading
page reads `acknowledgedAt` in `seedApprovals()`, which it already did. And
`classifySession()` now reads it too, which is a pre-existing bug fixed here:
acknowledging on one device cleared the alert everywhere except `codeman tui`.
It re-arms for free, because the next idle prompt supersedes the item and is
built fresh. Only `idle` is eligible, so a dialog that blocks the agent still
goes red whatever else it started.

The label is pane-derived and therefore prompt-injectable, so it is now read
from the last two rows of the screen only, with Claude's pattern anchored on
the `·` its footer joins items with, ANSI-stripped and length-capped at the
source. An agent that prints `· 1 monitor ·` into its own output finds no
match.

Verified on an isolated beta: a session that armed a monitor took its idle
prompt acknowledged with no alert on any surface, wore the badge, and showed
"quiet, watching 1 monitor" on its still-answerable card; the same session with
the monitor killed alerted normally on the next prompt. `test/watching-no-alert.test.ts`
pins both directions across all four surfaces.

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

src/session.ts

@@ -498,7 +498,21 @@ export class Session extends EventEmitter {
   private _activityStreak: ActivityStreak | null = null; // Unbroken run of PTY repaints (working detection)
   private _lastPaneProbeAt = 0; // Throttle for the tmux screen probe
   private _lastPaneProbeWorking: boolean | null = null; // Its last verdict (null = could not read)
-  private _watching: string | null = null; // Background work the pane's own footer reports
+  /**
+   * Background work the pane's own footer reports, e.g. `1 monitor`; null for none.
+   *
+   * Cached BESIDE `_lastPaneProbeWorking` and refreshed only by a capture that really
+   * happened, so it goes stale exactly as that verdict does. The probe returns its
+   * cached boolean without re-capturing inside `PANE_PROBE_MIN_INTERVAL_MS`, and a
+   * label derived from a capture nobody took would be a guess wearing a fact's clothes.
+   *
+   * ⚠️ It then FREEZES once `_confirmIdle()` concludes: `activityTimeout` is null from
+   * there, and nothing looks at the pane again until it produces output. That is
+   * correct rather than merely tolerable, because the background work ending is itself
+   * what wakes the agent and repaints the pane. Do not add a timer to keep this fresh;
+   * it would spend a `capture-pane` per idle session per tick to learn nothing.
+   */
+  private _watching: string | null = null;
   /** Lazily compiled `capabilities.workDetect.workingLine`. See _workingLinePattern(). */
   private _workingLineRe: RegExp | undefined = undefined;
   /** Lazily compiled `capabilities.workDetect.watchingLine`. See _watchingLinePattern(). */
@@ -2743,6 +2757,8 @@ export class Session extends EventEmitter {
    */
   private _readWatching(paneText: string | null): void {
     const pattern = this._watchingLinePattern();
+    // Called only from the probe, and only with what a capture returned: `null` is
+    // "the screen could not be read", which is not evidence that nothing is running.
     if (!pattern || paneText === null) return;
     this._watching = watchingLabel(paneText, pattern);
   }