feat(split): Pane B reconnects as soon as the server is back

When SSE comes back after a server restart, handleInit's reconnect
branch already re-opens the primary pane's socket; it now also calls
the split pane tile's reconnectNow(), so Pane B no longer waits out its
backoff (up to 10 s between tries) after every deploy. Live: Pane B was
back 4.6 s after the server process respawned, i.e. as soon as it
listened.

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

src/web/public/app.js

@@ -4581,6 +4581,10 @@ class CodemanApp {
         // a give-up) nothing else would re-establish it from here.
         if (this._wsSessionId !== restoreId) this._connectWs(restoreId);
         void this._onSessionNeedsRefresh({ id: restoreId });
+        // The split pane's second terminal reconnects on its own backoff (up to
+        // 10 s between tries); the server is back now, so skip the wait. A no-op
+        // while its socket is open, stopped for good, or destroyed.
+        this._splitPane?.reconnectNow?.();
       } else {
         this.activeSessionId = null;
         // `auto`: the app is restoring a session on load, not a human opening

test/terminal-tile-input.test.ts

@@ -676,3 +676,16 @@ describe('TerminalTile claims the keyboard for the app-level shortcuts', () => {
     expect(term.focusListeners).toEqual([]);
   });
 });
+
+describe('the server coming back kicks Pane B', () => {
+  it("handleInit's reconnect branch asks the split pane's tile to reconnect without waiting out its backoff", () => {
+    // handleInit needs a whole app to run, so the wiring is pinned by source;
+    // reconnectNow() itself is exercised above.
+    const appSource = readFileSync(resolve(import.meta.dirname, '../src/web/public/app.js'), 'utf8');
+    const start = appSource.indexOf('if (keepTerminal && restoreId === previousActiveId');
+    const branch = appSource.slice(start, appSource.indexOf('} else {', start));
+
+    expect(start).toBeGreaterThan(-1);
+    expect(branch).toContain('this._splitPane?.reconnectNow?.();');
+  });
+});