Add close button functionality to project tabs in Claude IDE

Fix missing 'x' close buttons on project tabs (Level 1). Session tabs
( Level 2) already had close buttons implemented.

Changes:
- project-manager.js: Added close button element to renderProjectTab()
- Added closeProject() method with confirmation dialog
- Added getSessionName() helper for session name display
- Auto-switches to next project when active project is closed
- project-tabs.css: Added .tab-close styling for project tabs
- Close button shows on hover, red highlight on hover
- Mobile responsive: always visible on small screens

The close button removes project tab from view but sessions remain
accessible via API/reload. Confirmation shows session count and list
for non-empty projects.

Resolves: https://rommark.dev/claude/ide/session/session-1769083280612-mdof554ot

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

public/claude-ide/project-tabs.css

@@ -98,6 +98,29 @@
     color: #4a9eff;
 }
 
+.project-tab .tab-close {
+    opacity: 0;
+    font-size: 16px;
+    line-height: 1;
+    width: 18px;
+    height: 18px;
+    display: flex;
+    align-items: center;
+    justify-content: center;
+    border-radius: 4px;
+    flex-shrink: 0;
+    transition: all 0.2s ease;
+}
+
+.project-tab:hover .tab-close {
+    opacity: 1;
+}
+
+.project-tab .tab-close:hover {
+    background: rgba(255, 107, 107, 0.2);
+    color: #ff6b6b;
+}
+
 /* New Project Tab */
 .project-tab-new {
     color: #51cf66;
@@ -391,6 +414,10 @@
         display: none;
     }
 
+    .project-tab .tab-close {
+        opacity: 1;
+    }
+
     .session-tab .tab-close {
         opacity: 1;
     }