Add logout button to header

Adds a logout button in the top bar on authenticated pages. Posts to
/api/auth/logout to clear the server session, then redirects to login.

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

app/templates/base.html

@@ -29,6 +29,9 @@
                 <div class="pending-count" id="pendingCount" style="display: none;">
                     <span id="pendingCountValue">0</span>
                 </div>
+                {% if show_nav %}
+                <button class="logout-btn" id="logoutBtn" title="Log out">Logout</button>
+                {% endif %}
             </div>
         </div>
     </header>