feat(cli): Antigravity run mode

Adds Antigravity as a sixth CLI backend alongside Claude Code, shell, OpenCode,
Codex and Gemini, following the existing pluggable-resolver pattern.

- `utils/antigravity-cli-resolver.ts` resolves the CLI, mirroring the other
  resolvers; `GET /api/antigravity/status` reports availability and path.
- `ANTIGRAVITY_*` joins the `ALLOWED_ENV_PREFIXES` allowlist in schemas.ts, so
  env overrides stay CLI-scoped rather than blanket-forwarded.
- Session, tmux-manager, mux-interface and types carry the new mode; secrets are
  injected via socket-scoped `tmux setenv`, never on the spawn command line, so
  the mode requires tmux with no direct PTY fallback like the other external CLIs.
- Frontend: Run-dropdown entry, agent-type option, `ag` tab badge and toolbar
  colours. `runAntigravity()` routes remote/docker cases through
  `POST /api/quick-start` and skips the local status probe for them.

Tests: test/antigravity-mode.test.ts, plus run-mode-ui and system-routes coverage.

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

src/web/routes/system-routes.ts

@@ -374,7 +374,7 @@ export function registerSystemRoutes(
   });
 
   // ═══════════════════════════════════════════════════════════════
-  // CLI Integrations (OpenCode, Codex, Gemini)
+  // CLI Integrations (OpenCode, Codex, Gemini, Antigravity)
   // ═══════════════════════════════════════════════════════════════
 
   // ========== OpenCode ==========
@@ -405,6 +405,16 @@ export function registerSystemRoutes(
     };
   });
 
+  // ========== Antigravity ==========
+
+  app.get('/api/antigravity/status', async () => {
+    const { isAntigravityAvailable, resolveAntigravityDir } = await import('../../utils/antigravity-cli-resolver.js');
+    return {
+      available: isAntigravityAvailable(),
+      path: resolveAntigravityDir(),
+    };
+  });
+
   // ═══════════════════════════════════════════════════════════════
   // State & Lifecycle (cleanup, lifecycle log, stats)
   // ═══════════════════════════════════════════════════════════════