fix(approvals): merge-time fixes for the watching badge (#473)

- session.ts: a pane capture that fails now CLEARS the watching label
  (and emits watchingChanged so pages drop the badge) instead of keeping
  the last one, so a failed capture degrades toward an alert rather than
  pre-acknowledging the next real idle prompt. Test updated; invariant
  noted in architecture-invariants.
- approvals-ui.js: the header bell counts only unacknowledged items
  (pendingApprovalsCount), matching codeman tui's pendingApprovalCount();
  pinned in watching-no-alert.test.ts.
- mobile-overview.js: move the orphaned "Pill copy per state" JSDoc back
  onto MOBILE_OVERVIEW_PILL_LABEL.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

src/session.ts

@@ -2991,15 +2991,18 @@ export class Session extends EventEmitter {
    * capture at exactly the moment the turn ends, which is the moment the answer starts
    * mattering.
    *
-   * A capture that could not be read leaves the last answer standing, the way the
-   * working probe treats its own null: no evidence is not evidence of none.
+   * A capture that could not be read CLEARS the label rather than keeping the last one.
+   * The two wrong answers are not symmetric: a stale label opens the next idle prompt
+   * already acknowledged, so a failed capture would silence a real alert, while a dropped
+   * label only costs a card and an alert that the next readable capture takes back.
+   * Degrading toward the alert is the rule the whole signal is built on.
    */
   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;
-    const label = watchingLabel(paneText, pattern, this._watchingWindow);
+    if (!pattern) return;
+    // `null` is "the screen could not be read". That is no evidence either way, so the
+    // label falls to null (and the change is announced below like any other).
+    const label = paneText === null ? null : watchingLabel(paneText, pattern, this._watchingWindow);
     if (label === this._watching) return;
     this._watching = label;
     // ⚠️ This CHANGES while the session's status does not, so it needs an event of its

src/web/public/approvals-ui.js

@@ -194,8 +194,21 @@ Object.assign(CodemanApp.prototype, {
     document.querySelector('.btn-approvals')?.setAttribute('aria-expanded', 'false');
   },
 
+  /**
+   * Items still waiting on a human. An acknowledged item (a human already looked, or the
+   * session opened it acknowledged because it is watching its own background work) keeps
+   * its card but arms no alert, so it must not light the bell either; this is the same
+   * count `pendingApprovalCount()` gives `codeman tui`.
+   */
+  pendingApprovalsCount() {
+    if (!this.approvals) return 0;
+    let count = 0;
+    for (const item of this.approvals.values()) if (!item.acknowledgedAt) count++;
+    return count;
+  },
+
   renderApprovals() {
-    const count = this.approvals ? this.approvals.size : 0;
+    const count = this.pendingApprovalsCount();
     const btn = document.querySelector('.btn-approvals');
     if (btn) {
       // Marker-class visibility (base header rules are display !important):

src/web/public/mobile-overview.js

@@ -60,7 +60,6 @@ const MOBILE_OVERVIEW_RUN_MODES = [
   { mode: 'shell', label: 'Terminal / Shell', short: 'Shell' },
 ];
 
-/** Pill copy per state. Kept short: a phone row has ~90px for it. */
 /**
  * The one word every surface puts on the watching badge, and the tooltip that says
  * what the pane actually reported. Both live here so the phone overview, the desktop
@@ -69,6 +68,7 @@ const MOBILE_OVERVIEW_RUN_MODES = [
 const WATCHING_BADGE_TEXT = 'watching';
 const watchingBadgeTitle = (label) => 'Still running in the background: ' + label;
 
+/** Pill copy per state. Kept short: a phone row has ~90px for it. */
 const MOBILE_OVERVIEW_PILL_LABEL = {
   needs: 'needs you',
   error: 'error',