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/public/index.html

@@ -311,11 +311,11 @@
           <h1 class="welcome-title">Codeman</h1>
           <p class="welcome-desc">Manage AI Coding tools in persistent tmux sessions.</p>
           <div class="welcome-actions">
-            <button class="welcome-btn welcome-btn-claude" onclick="app.setRunMode('claude'); app.runClaude()">
+            <button class="welcome-btn welcome-btn-claude" id="welcomeClaudeBtn" style="display: none;" onclick="app.setRunMode('claude'); app.runClaude()">
               <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><polygon points="5 3 19 12 5 21 5 3"/></svg>
               Run Claude Code
             </button>
-            <button class="welcome-btn welcome-btn-opencode" onclick="app.setRunMode('opencode'); app.runOpenCode()">
+            <button class="welcome-btn welcome-btn-opencode" id="welcomeOpencodeBtn" style="display: none;" onclick="app.setRunMode('opencode'); app.runOpenCode()">
               <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><polygon points="5 3 19 12 5 21 5 3"/></svg>
               Run OpenCode
             </button>

src/web/public/settings-ui.js

@@ -695,10 +695,22 @@ Object.assign(CodemanApp.prototype, {
   },
 
   async loadGeminiAvailability() {
-    const btn = document.getElementById('welcomeGeminiBtn');
+    await this._loadCliAvailability('welcomeGeminiBtn', '/api/gemini/status');
+  },
+
+  async loadClaudeAvailability() {
+    await this._loadCliAvailability('welcomeClaudeBtn', '/api/claude/status');
+  },
+
+  async loadOpencodeAvailability() {
+    await this._loadCliAvailability('welcomeOpencodeBtn', '/api/opencode/status');
+  },
+
+  async _loadCliAvailability(buttonId, statusUrl) {
+    const btn = document.getElementById(buttonId);
     if (!btn) return;
     try {
-      const res = await fetch('/api/gemini/status');
+      const res = await fetch(statusUrl);
       const env = await res.json();
       const status = env?.success === true ? env.data : env;
       btn.style.display = status?.available ? 'flex' : 'none';

src/web/public/terminal-ui.js

@@ -1195,6 +1195,8 @@ Object.assign(CodemanApp.prototype, {
     if (overlay) {
       overlay.classList.add('visible');
       this.loadTunnelStatus();
+      this.loadClaudeAvailability();
+      this.loadOpencodeAvailability();
       this.loadGeminiAvailability();
       this.loadHistorySessions();
       this.initSearchPanel();

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 () => {