fix(run,terminal): merge-time fixes for the Instance count stepper and capture geometry

#454: the behaviour the PR adds had no test, so a regression test drives
runGrok() at tabCount 3 and asserts three quick-start POSTs with sequential
w<n>-<case> names (verified to fail against master's session-ui.js). Each
caller now reads the count BEFORE its opening banner and announces it there,
the way runClaude() already did, so a launch no longer prints two headers and
a launch with another session already active still says how many are starting.
runClaude() calls the shared _readTabCount() instead of its own copy of the
1..20 clamp, and that helper optional-chains the element read, since hoisting
it above each caller's try block would otherwise let a missing #tabCount throw
where the launch-error path cannot report it.

#435: sizeMovedUnderLoad derived from data.source alone. `mux-visible` is not
sufficient: a failed display-message cursor query makes capturePaneBuffer skip
the snapshot repaint and return the raw capture, which the route still labels
mux-visible, so a size that moved during such a load bought a full forced
reload to repair a frame that was never positioned. It now tests
Number.isFinite(data.captureRows) like its two siblings.

Plus the invariants and CLAUDE.md lines promised on #435: a visible capture
reports its geometry and omits it when nothing was positioned, the comparison
runs on mux-visible only, and the replay is capped at one attempt and latches
per session when it cannot converge.

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

test/run-mode-ui.test.ts

@@ -1122,4 +1122,67 @@ describe('Grok quick start', () => {
     expect(requests).toEqual(['/api/grok/status']);
     expect(errors[0]).toContain('https://x.ai/cli/install.sh');
   });
+
+  // The whole point of the shared _launchQuickStartInstances() helper. Before it,
+  // every non-Claude run*() hardcoded exactly one quick-start call, so the
+  // "Instance count" stepper next to the Run button silently did nothing on all
+  // eight of them: no error, no hint, just the wrong number of sessions. The five
+  // fixture edits that came with the change stub tabCount at '1', so they pass
+  // identically with and without it; this is the one that does not.
+  it('launches tabCount sessions with sequential w<n>-<case> names and selects the first', async () => {
+    const elements: Record<string, any> = {
+      quickStartCase: { value: 'grok-case' },
+      tabCount: { value: '3' },
+    };
+    const requests: Array<{ url: string; body?: any }> = [];
+    const CodemanApp = function CodemanApp(this: any) {};
+    let created = 0;
+
+    const context = vm.createContext({
+      CodemanApp,
+      localStorage: { getItem: () => null, setItem: () => {} },
+      document: { getElementById: (id: string) => elements[id] ?? null },
+      fetch: async (url: string, init?: { body?: string }) => {
+        const body = init?.body ? JSON.parse(init.body) : undefined;
+        requests.push({ url, body });
+        if (url === '/api/grok/status')
+          return {
+            json: async () => ({
+              success: true,
+              data: { available: true, path: '/home/user/.grok/bin', version: '1.0.5' },
+            }),
+          };
+        if (url === '/api/quick-start') {
+          const id = `sess-gk-${created++}`;
+          return {
+            json: async () => ({ success: true, data: { sessionId: id, session: { id, name: body.sessionName } } }),
+          };
+        }
+        throw new Error(`unexpected fetch: ${url}`);
+      },
+      console,
+    });
+
+    const sessionUi = readFileSync(resolve(import.meta.dirname, '../src/web/public/session-ui.js'), 'utf8');
+    vm.runInContext(sessionUi, context, { filename: 'session-ui.js' });
+
+    const app = new (CodemanApp as any)();
+    app.terminal = { clear: () => {}, writeln: () => {}, focus: () => {} };
+    app.loadAppSettingsFromStorage = () => ({});
+    app.getCaseSettings = () => ({});
+    app.buildEnvOverrides = () => ({});
+    app.sessions = new Map();
+    app._onSessionCreated = (session: any) => app.sessions.set(session.id, session);
+    app._renderSessionTabsImmediate = () => {};
+    const selected: string[] = [];
+    app.selectSession = async (id: string) => {
+      selected.push(id);
+    };
+
+    await app.runGrok();
+
+    const names = requests.filter((r) => r.url === '/api/quick-start').map((r) => r.body.sessionName);
+    expect(names).toEqual(['w1-grok-case', 'w2-grok-case', 'w3-grok-case']);
+    expect(selected).toEqual(['sess-gk-0']);
+  });
 });