docs: update project documentation for GStack Browser improvements

README.md: updated Real browser mode and sidebar agent sections with
model routing, cookie import button, no idle timeout in headed mode.
Updated skill table entries for /browse and /open-gstack-browser.

docs/skills.md: updated /open-gstack-browser deep dive with model
routing and cookie import details.

GSTACK_BROWSER_V0.md: added 6 new SHIPPED items to implementation
status table (model routing, debug logging, idle timeout, cookie
button, arrow hint, architecture doc).

TODOS.md: marked "Sidebar agent Write tool + error visibility" as
SHIPPED. Added new P2 TODO for direct API calls to eliminate
claude -p startup tax.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

docs/designs/GSTACK_BROWSER_V0.md

@@ -319,8 +319,14 @@ From DESIGN.md:
 | DMG packaging | **SHIPPED** | 189MB compressed |
 | `GSTACK_CHROMIUM_PATH` | **SHIPPED** | Custom Chromium binary support |
 | `BROWSE_EXTENSIONS_DIR` | **SHIPPED** | Extension path override |
-| Auth via `/health` | **SHIPPED** | Replaces .auth.json file approach |
+| Auth via `/health` | **SHIPPED** | Replaces .auth.json file approach, auto-refreshes on server restart |
 | Build script | **SHIPPED** | `scripts/build-app.sh` |
+| Model routing | **SHIPPED** | Sonnet for actions, Opus for analysis (`pickSidebarModel`) |
+| Debug logging | **SHIPPED** | 40+ silent catches → prefixed console logging across 4 files |
+| No idle timeout (headed) | **SHIPPED** | Browser stays alive as long as window is open |
+| Cookie import button | **SHIPPED** | One-click in sidebar footer, opens `/cookie-picker` |
+| Sidebar arrow hint | **SHIPPED** | Points to sidebar, hides only when sidebar actually opens |
+| Architecture doc | **SHIPPED** | `docs/designs/SIDEBAR_MESSAGE_FLOW.md` |
 | Command palette | Planned | Phase 1b |
 | Quick screenshot | Planned | Phase 1b |
 | Status bar | Planned | Phase 1b |