Add login modal to landing page

- Show login modal when user is not authenticated
- Add handleLogin, showLoginModal, closeLoginModal functions
- Add login modal HTML with username/password form
- Add CSS styles for modal

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

public/claude-ide/projects-landing.css

@@ -417,3 +417,115 @@ body.sessions-page {
         padding-top: 80px;
     }
 }
+
+/* === Login Modal === */
+.modal {
+    display: none;
+    position: fixed;
+    top: 0;
+    left: 0;
+    width: 100%;
+    height: 100%;
+    background: rgba(0, 0, 0, 0.8);
+    justify-content: center;
+    align-items: center;
+    z-index: 10000;
+}
+
+.modal-content {
+    background: #1a1a1a;
+    border: 1px solid #333;
+    border-radius: 12px;
+    padding: 0;
+    width: 100%;
+    max-width: 400px;
+    box-shadow: 0 10px 40px rgba(0, 0, 0, 0.5);
+}
+
+.modal-header {
+    display: flex;
+    justify-content: space-between;
+    align-items: center;
+    padding: 20px 24px;
+    border-bottom: 1px solid #333;
+}
+
+.modal-header h2 {
+    margin: 0;
+    font-size: 18px;
+    color: #e0e0e0;
+}
+
+.modal-close {
+    background: none;
+    border: none;
+    color: #888;
+    font-size: 24px;
+    cursor: pointer;
+    padding: 0;
+    width: 32px;
+    height: 32px;
+    display: flex;
+    align-items: center;
+    justify-content: center;
+}
+
+.modal-close:hover {
+    color: #fff;
+}
+
+.modal-body {
+    padding: 24px;
+}
+
+.form-group {
+    margin-bottom: 16px;
+}
+
+.form-group label {
+    display: block;
+    margin-bottom: 6px;
+    color: #aaa;
+    font-size: 13px;
+}
+
+.form-group input {
+    width: 100%;
+    padding: 10px 12px;
+    background: #0d0d0d;
+    border: 1px solid #333;
+    border-radius: 6px;
+    color: #e0e0e0;
+    font-size: 14px;
+}
+
+.form-group input:focus {
+    outline: none;
+    border-color: #4a9eff;
+}
+
+.btn-primary {
+    width: 100%;
+    padding: 12px;
+    background: #4a9eff;
+    color: white;
+    border: none;
+    border-radius: 6px;
+    font-size: 14px;
+    font-weight: 600;
+    cursor: pointer;
+}
+
+.btn-primary:hover {
+    background: #3a8eef;
+}
+
+.login-error {
+    margin-bottom: 16px;
+    padding: 10px 12px;
+    background: rgba(255, 107, 107, 0.1);
+    border: 1px solid #ff6b6b;
+    border-radius: 6px;
+    color: #ff6b6b;
+    font-size: 13px;
+}