fix(welcome): gate Gemini button on availability, drop unconditional tunnel button

- Remove the always-visible Cloudflare Tunnel welcome button and QR
  widget; offering it regardless of whether cloudflared is installed
  is a bad default.
- Hide the "Run Gemini" welcome button by default and only show it
  when /api/gemini/status reports available:true, via new
  loadGeminiAvailability() called from showWelcome().

src/web/public/index.html

@@ -315,23 +315,15 @@
               <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-tunnel" id="welcomeTunnelBtn" onclick="app.toggleTunnelFromWelcome()">
-              <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><path d="M12 2L2 7l10 5 10-5-10-5z"/><path d="M2 17l10 5 10-5"/><path d="M2 12l10 5 10-5"/></svg>
-              Cloudflare Tunnel
-            </button>
             <button class="welcome-btn welcome-btn-opencode" 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>
-            <button class="welcome-btn welcome-btn-gemini" onclick="app.setRunMode('gemini'); app.runGemini()">
+            <button class="welcome-btn welcome-btn-gemini" id="welcomeGeminiBtn" style="display: none;" onclick="app.setRunMode('gemini'); app.runGemini()">
               <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 Gemini
             </button>
           </div>
-          <div class="welcome-qr" id="welcomeQr" onclick="app.toggleWelcomeQrSize()">
-            <div class="welcome-qr-inner" id="welcomeQrInner"></div>
-            <div class="welcome-qr-url" id="welcomeQrUrl"></div>
-          </div>
           <div class="history-sessions" id="historySessions" style="display:none">
             <div class="search-panel" id="searchPanel">
               <div class="search-input-row">

src/web/public/settings-ui.js

@@ -694,6 +694,19 @@ Object.assign(CodemanApp.prototype, {
     this._updatePollTimer = setInterval(poll, 1500);
   },
 
+  async loadGeminiAvailability() {
+    const btn = document.getElementById('welcomeGeminiBtn');
+    if (!btn) return;
+    try {
+      const res = await fetch('/api/gemini/status');
+      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 loadTunnelStatus() {
     try {
       const res = await fetch('/api/tunnel/status');

src/web/public/terminal-ui.js

@@ -1195,6 +1195,7 @@ Object.assign(CodemanApp.prototype, {
     if (overlay) {
       overlay.classList.add('visible');
       this.loadTunnelStatus();
+      this.loadGeminiAvailability();
       this.loadHistorySessions();
       this.initSearchPanel();
     }