feat: connected accounts + Gemini API key in account settings UI

Settings page gains two new sections:
- Connected Accounts: shows linked Google email (read-only)
- Gemini API Key: paste personal key from aistudio.google.com,
  shows masked hint of saved key, remove link to revert to server key

POST /settings/gemini-key saves/clears gemini_api_key in auth.json.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

cortex/static/settings.html

@@ -232,6 +232,45 @@
       </form>
     </div>
 
+    <!-- Connected accounts -->
+    <div class="section">
+      <h2>Connected Accounts</h2>
+      <div class="field">
+        <label>Google Account</label>
+        <input type="text" value="{{ google_email }}" readonly
+               placeholder="No Google account linked"
+               style="{{ google_email == '' and 'color:#475569' or '' }}">
+      </div>
+      <p style="font-size:0.75rem; color:#94a3b8; margin-top:-0.5rem;">
+        To link or change your Google account, contact Scott.
+      </p>
+    </div>
+
+    <!-- Gemini API key -->
+    <div class="section">
+      <h2>Gemini API Key</h2>
+      <p style="font-size:0.8rem; color:#94a3b8; margin-bottom:0.85rem; line-height:1.55;">
+        Paste your personal key from
+        <a href="https://aistudio.google.com/apikey" target="_blank" rel="noopener"
+           style="color:#a78bfa;">aistudio.google.com/apikey</a>
+        to use your own Gemini quota. Leave blank to use the shared server key.
+      </p>
+      <form method="POST" action="/settings/gemini-key">
+        <div class="field">
+          <label for="gemini_api_key">API Key</label>
+          <input type="password" id="gemini_api_key" name="gemini_api_key"
+                 placeholder="{{ gemini_key_hint }}" autocomplete="off">
+        </div>
+        <button type="submit">Save Key</button>
+      </form>
+      <p id="gemini-key-status" style="font-size:0.75rem; color:#94a3b8; margin-top:0.5rem;">
+        Current: {{ gemini_key_hint }}
+        <span id="gemini-remove-wrap" style="{{ gemini_key_set == 'false' and 'display:none' or '' }}">
+          — <a href="#" id="gemini-remove-link" style="color:#f87171;">remove</a>
+        </span>
+      </p>
+    </div>
+
     <!-- Change password -->
     <div class="section">
       <h2>Change Password</h2>
@@ -287,6 +326,16 @@
       document.getElementById('show-rename-user').style.display = '';
     });
 
+    // Gemini key — "remove" link clears the input and submits the form
+    const geminiRemove = document.getElementById('gemini-remove-link');
+    if (geminiRemove) {
+      geminiRemove.addEventListener('click', e => {
+        e.preventDefault();
+        document.getElementById('gemini_api_key').value = '';
+        document.querySelector('form[action="/settings/gemini-key"]').submit();
+      });
+    }
+
     // Persona rename toggle
     document.querySelectorAll('.persona-rename-toggle').forEach(btn => {
       btn.addEventListener('click', () => {