fix(run-mode): gate dropdown entries on CLI availability

Follow-up to the welcome-screen gating (#200): the run-mode dropdown
(gear menu next to Run) had the same problem — Claude/Opencode/Codex/
Gemini entries were always shown regardless of whether the CLI is
actually installed, so picking one could spawn a session that
immediately errors out.

- Add _refreshRunModeAvailability() (session-ui.js), called each time
  the dropdown opens; hides entries whose /api/<cli>/status reports
  unavailable.
- Shell is intentionally never gated (no external CLI dependency).

Depends on isClaudeAvailable()/GET /api/claude/status, which don't
exist on upstream/master yet — duplicated here from #200 so this PR
is self-contained and independently mergeable. Once #200 lands this
branch should be rebased onto master, which will collapse the
duplicate cleanly.

src/utils/claude-cli-resolver.ts

@@ -26,6 +26,15 @@ const CLAUDE_SEARCH_DIRS = [
 /** Cached directory containing the claude binary (empty string = searched but not found) */
 let _claudeDir: string | null = null;
 
+/**
+ * Returns true if the Claude CLI binary can be located (via `which` or one of
+ * the common install directories). Mirrors `isGeminiAvailable`/`isOpenCodeAvailable`/
+ * `isCodexAvailable` in the sibling resolvers.
+ */
+export function isClaudeAvailable(): boolean {
+  return findClaudeDir() !== null;
+}
+
 /**
  * Finds the directory containing the `claude` binary.
  * Checks `which claude` first, then falls back to common install locations.

src/web/public/session-ui.js

@@ -441,6 +441,7 @@ Object.assign(CodemanApp.prototype, {
     // Load history sessions when menu opens
     if (menu.classList.contains('active')) {
       this._loadRunModeHistory();
+      this._refreshRunModeAvailability();
       const close = (ev) => {
         if (!menu.contains(ev.target)) {
           menu.classList.remove('active');
@@ -451,6 +452,32 @@ Object.assign(CodemanApp.prototype, {
     }
   },
 
+  /**
+   * Hides run-mode dropdown entries for CLIs that aren't installed, so
+   * picking one doesn't spawn a session that immediately errors out.
+   * Shell has no external CLI dependency and is never gated.
+   */
+  async _refreshRunModeAvailability() {
+    const checks = [
+      ['claude', '/api/claude/status'],
+      ['opencode', '/api/opencode/status'],
+      ['codex', '/api/codex/status'],
+      ['gemini', '/api/gemini/status'],
+    ];
+    await Promise.all(checks.map(async ([mode, url]) => {
+      const btn = document.querySelector(`.run-mode-option[data-mode="${mode}"]`);
+      if (!btn) return;
+      try {
+        const res = await fetch(url);
+        const env = await res.json();
+        const status = env?.success === true ? env.data : env;
+        btn.style.display = status?.available ? 'flex' : 'none';
+      } catch {
+        btn.style.display = 'none';
+      }
+    }));
+  },
+
   async _loadRunModeHistory() {
     const container = document.getElementById('runModeHistory');
     if (!container) return;

src/web/routes/system-routes.ts

@@ -374,9 +374,19 @@ export function registerSystemRoutes(
   });
 
   // ═══════════════════════════════════════════════════════════════
-  // CLI Integrations (OpenCode, Codex, Gemini, Antigravity)
+  // CLI Integrations (Claude, OpenCode, Codex, Gemini, Antigravity)
   // ═══════════════════════════════════════════════════════════════
 
+  // ========== Claude ==========
+
+  app.get('/api/claude/status', async () => {
+    const { isClaudeAvailable, findClaudeDir } = await import('../../utils/claude-cli-resolver.js');
+    return {
+      available: isClaudeAvailable(),
+      path: findClaudeDir(),
+    };
+  });
+
   // ========== OpenCode ==========
 
   app.get('/api/opencode/status', async () => {