feat(management): extract repository management into dashboard component

Move the inline repository management UI into a new RepositoryDashboard component
and wire it into the application. Refactor app state to compute a reactive
dashboardRepos list and update tab-closing logic so tabs can be closed while
preserving the management view when appropriate.

- Add a full dashboard with search, categories, workspaces and persisted prefs.
- Refactor close behavior to support keeping the management view open.
- Improve UI/CSS and accessibility for the management tab (compact layout and label).

src/app.css

@@ -9050,3 +9050,12 @@ input:focus, textarea:focus, select:focus { box-shadow: 0 0 0 3px color-mix(in s
   border-color: #a9212b;
   background: #c92f3a;
 }
+
+/* Keep the repository overview as a compact icon tab. */
+.repo-tab.management {
+  flex: 0 0 38px;
+  width: 38px;
+  min-width: 38px;
+  padding: 0;
+  justify-content: center;
+}