fix(welcome): gate Claude and Opencode buttons on CLI availability too

Extends the Gemini gating from bb7fb9e to the other welcome-screen
buttons that had the same problem: shown unconditionally even when the
underlying CLI isn't installed.

- Add isClaudeAvailable() (claude-cli-resolver.ts) and GET
  /api/claude/status, mirroring the existing opencode/codex/gemini
  resolvers and status endpoints.
- Opencode already had a working /api/opencode/status the welcome
  screen just wasn't checking; wire it up the same way.
- Refactor loadGeminiAvailability() into a shared
  _loadCliAvailability(buttonId, statusUrl) helper instead of
  duplicating the fetch/try-catch three times.

Run-mode dropdown entries (Opencode/Codex) are intentionally left
unconditional here — follow-up PR.

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 () => {