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/public/index.html

@@ -464,6 +464,9 @@
               <button class="run-mode-option" data-mode="gemini" onclick="app.setRunMode('gemini')">
                 <span class="run-mode-dot gemini"></span>Gemini
               </button>
+              <button class="run-mode-option" data-mode="antigravity" onclick="app.setRunMode('antigravity')">
+                <span class="run-mode-dot antigravity"></span>Antigravity
+              </button>
               <div class="run-mode-sep"></div>
               <button class="run-mode-option" data-mode="shell" onclick="app.setRunMode('shell')">
                 <span class="run-mode-dot shell"></span>Terminal / Shell
@@ -733,6 +736,7 @@
                 <option value="opencode">OpenCode</option>
                 <option value="codex">Codex</option>
                 <option value="gemini">Gemini</option>
+                <option value="antigravity">Antigravity</option>
               </select>
             </div>
             <div class="form-row"><label>Working Directory</label><input type="text" id="schWorkingDir" placeholder="/absolute/path"></div>