Fix missing header buttons for Arc-style vertical tabs

- Add currentUser and authMethod properties to header-base component
- Add event handlers for file browser, notifications, and logout
- Add missing utility buttons (Browse Files, Notifications, Logout) to full-header
- Add Browse Files button to sidebar-header for compact mode
- Import notification-status component in full-header

This restores the missing functionality mentioned in the PR review.

web/src/client/components/full-header.ts

@@ -187,4 +187,4 @@ export class FullHeader extends HeaderBase {
       </div>
     `;
   }
-}
+}

web/src/client/components/header-base.ts

@@ -66,6 +66,14 @@ export abstract class HeaderBase extends LitElement {
     );
   }
 
+  protected handleOpenFileBrowser() {
+    this.dispatchEvent(new CustomEvent('open-file-browser'));
+  }
+
+  protected handleOpenNotificationSettings() {
+    this.dispatchEvent(new CustomEvent('open-notification-settings'));
+  }
+
   protected handleLogout() {
     this.showUserMenu = false;
     this.dispatchEvent(new CustomEvent('logout'));
@@ -91,4 +99,4 @@ export abstract class HeaderBase extends LitElement {
     super.disconnectedCallback();
     document.removeEventListener('click', this.handleClickOutside);
   }
-}
+}

web/src/client/components/sidebar-header.ts

@@ -51,6 +51,13 @@ export class SidebarHeader extends HeaderBase {
             </button>
 
             <div class="flex flex-col gap-1 w-full max-w-[200px]">
+              <button
+                class="btn-ghost font-mono text-xs px-3 py-1.5 w-full"
+                @click=${this.handleOpenFileBrowser}
+                title="Browse files"
+              >
+                Browse Files
+              </button>
               ${this.renderExitedToggleButton(exitedSessions, true)}
               ${this.renderActionButtons(exitedSessions, runningSessions, true)}
             </div>