Open on startup by default and block duplicate workspace names

- LoginItem registers on the first bundled launch, so the app opens on
  startup without the user finding the toggle; a user who turns it off is
  never overridden. A never-registered bundle reports SMAppService .notFound
  rather than .notRegistered, so the guard only treats enabled/approval as
  done. --diag now prints the raw status.
- New Workspace refuses a name that already exists (case-insensitive) and
  says so inline; Return cannot bypass it. The composer's '# Name' still
  switches to the existing workspace, which is the quick-capture gesture.

Sources/Prompt/PanelView.swift

@@ -616,6 +616,19 @@ struct PanelView: View {
 
     // MARK: - New workspace
 
+    private var trimmedWorkspaceName: String {
+        newWorkspaceName.trimmingCharacters(in: .whitespacesAndNewlines)
+    }
+
+    /// Case-insensitive, like the store's dedupe. The modal blocks creation
+    /// with a hint instead of silently switching to the existing workspace.
+    private var workspaceNameExists: Bool {
+        let name = trimmedWorkspaceName
+        return !name.isEmpty && store.sections.contains {
+            $0.name.caseInsensitiveCompare(name) == .orderedSame
+        }
+    }
+
     @ViewBuilder
     private var newWorkspaceModal: some View {
         if showNewWorkspace {
@@ -630,12 +643,17 @@ struct PanelView: View {
                         .focused($focusedField, equals: .newWorkspace)
                         .onSubmit(createWorkspace)
                         .onExitCommand { dismissNewWorkspace() }
+                    if workspaceNameExists {
+                        Text("A workspace named “\(trimmedWorkspaceName)” already exists.")
+                            .font(.caption)
+                            .foregroundStyle(.red)
+                    }
                     HStack {
                         Spacer()
                         Button("Cancel") { dismissNewWorkspace() }
                         Button("Create") { createWorkspace() }
                             .keyboardShortcut(.defaultAction)
-                            .disabled(newWorkspaceName.trimmingCharacters(in: .whitespaces).isEmpty)
+                            .disabled(trimmedWorkspaceName.isEmpty || workspaceNameExists)
                     }
                 }
                 .padding(16)
@@ -649,8 +667,8 @@ struct PanelView: View {
     }
 
     private func createWorkspace() {
-        let name = newWorkspaceName.trimmingCharacters(in: .whitespacesAndNewlines)
-        guard !name.isEmpty else { return }
+        let name = trimmedWorkspaceName
+        guard !name.isEmpty, !workspaceNameExists else { return }
         store.createSection(named: name)
         dismissNewWorkspace()
     }