feat(session): say when a session is watching its own background work

An agent that arms a monitor, backgrounds a shell or hands a task to a
cloud session is told to end its turn. The pane then falls quiet, Claude
Code's idle_prompt notification arrives a minute later, and every surface
files the session under NEEDS YOU with nothing for a human to answer.

Claude states what it is still running on the last row of its screen
(`⏵⏵ bypass permissions on · 1 monitor · ← for agents`). That row is now
`capabilities.workDetect.watchingLine` in the CLI registry, guarded by
compileVersionRegex() like every other config regex, and the idle probe
reads it off the capture it already takes: `watchingLabel()` in
session-activity.ts searches the last five lines only, so a session that
PRINTS "1 monitor" is not mistaken for one running it.

The label lands on Session.watching and rides toLightDetailedState() out
to every surface. The phone overview, the desktop home rail and the rich
sidebar rows wear it as a `watching` badge in the accent colour, beside
the state pill and never in place of it: an agent can arm a monitor and
ask a question in the same breath, and only the pill says which.

Verified end to end against a throwaway session on an isolated beta
instance: the payload carried `watching: "1 monitor"` once the turn
ended, the badge rendered next to a yellow `waiting` pill, and both
cleared when the monitor died.

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

test/session-sidebar-ux.test.ts

@@ -73,3 +73,35 @@ describe('vertical session navigation UX contract', () => {
     expect(i18n).toContain("'Adjust only session names in the vertical sidebar.':");
   });
 });
+
+describe('watching badge on a rich session row', () => {
+  it('reads the label off the session payload', () => {
+    expect(app).toContain("watching: typeof session.watching === 'string' ? session.watching : ''");
+  });
+
+  it('renders it beside the state pill rather than in place of it', () => {
+    // A session can be watching a monitor AND holding a question for the user, so the
+    // pill that says which one still decides the row; this badge only adds a fact.
+    const meta = app.slice(app.indexOf('_sidebarRichMetaHTML(row) {'));
+    const body = meta.slice(0, meta.indexOf('_sidebarRichStampText(timestamp, format) {'));
+    expect(body).toContain('tab-pill tab-pill--${escapeHtml(row.state)}');
+    expect(body).toContain('tab-pill tab-pill--watching');
+    expect(body).toContain('Still running in the background:');
+  });
+
+  it('re-renders the row when the background work changes', () => {
+    // The meta line is rebuilt only when this signature moves, so a badge left out of
+    // it would appear and disappear a render late, or not at all.
+    expect(app).toContain(
+      'const sig = `${row.state}:${row.since ? row.since.at : 0}:${row.createdAt}:${row.watching}`'
+    );
+  });
+
+  it('colours it with the accent, never with the two colours that mean a human is needed', () => {
+    const rule = styles.slice(styles.indexOf('.tab-pill--watching'));
+    const block = rule.slice(0, rule.indexOf('}'));
+    expect(block).toContain('var(--accent)');
+    expect(block).not.toContain('var(--red)');
+    expect(block).not.toContain('var(--yellow)');
+  });
+});