fix(desktop): keep the Sessions label when the grouped sidebar has no projects

The source-filter (grouped) toggle headed the sessions section
"Projects" whenever it was active, even when the project tree held no
real project: with no projects at all the section listed plain chat
sessions under a "Projects" header, and with only unclaimed sessions it
showed the synthetic Home bucket — the flat session list wearing a
project costume — under the same header.

Read the label from what the section actually shows: "Projects" while a
real project row exists or the tree is still resolving, "Sessions"
otherwise. Entering a project keeps showing the project's name.

Fixes #62537

Co-authored-by: giggling-ginger <110955495+giggling-ginger@users.noreply.github.com>

apps/desktop/src/app/chat/sidebar/chat-sidebar.integration.test.tsx

@@ -278,6 +278,73 @@ describe('ChatSidebar project entry', () => {
 // Messaging platforms group rows by owner the same way recents does once every
 // profile is on screen, so a Telegram thread is attributable to its profile
 // (#87715). The platform's row cap and load-more stay the section's.
+describe('ChatSidebar section labels', () => {
+  const realProject = {
+    id: '/repos/new-project',
+    label: 'new-project',
+    path: '/repos/new-project',
+    repos: [],
+    sessionCount: 0
+  }
+
+  // The synthetic Home bucket the backend emits when no project claimed a
+  // session (no cwd / deleted workspace): one lane, no repo structure.
+  const homeOnly = [
+    {
+      ...realProject,
+      id: '__no_project__',
+      label: 'Home',
+      path: null,
+      isNoProject: true,
+      sessionCount: 2
+    }
+  ]
+
+  afterEach(() => {
+    cleanup()
+    $projectScope.set(ALL_PROJECTS)
+    $projectTree.set([])
+    setSidebarAgentsGrouped(false)
+    $sessions.set([])
+  })
+
+  it('labels the section "Projects" when the grouped tree has a real project', () => {
+    setSidebarAgentsGrouped(true)
+    $projectTree.set([realProject])
+
+    renderSidebar('/', 'chat')
+
+    expect(screen.getByText('Projects')).toBeTruthy()
+    expect(screen.queryByText('Sessions')).toBeNull()
+  })
+
+  it('keeps the "Sessions" label when grouping is on but no projects exist', () => {
+    // The source-filter toggle with an empty tree: the section lists plain
+    // chat sessions, so heading it "Projects" mislabeled them (#62537).
+    setSidebarAgentsGrouped(true)
+    $projectTree.set([])
+    $sessions.set(sessionRows)
+
+    renderSidebar('/', 'chat')
+
+    expect(screen.getByText('Sessions')).toBeTruthy()
+    expect(screen.queryByText('Projects')).toBeNull()
+  })
+
+  it('keeps the "Sessions" label when the grouped tree is only the synthetic Home bucket', () => {
+    // No real projects — every session fell into Home. A lone Home bucket is
+    // the flat session list wearing a project costume, not a switcher.
+    setSidebarAgentsGrouped(true)
+    $projectTree.set(homeOnly)
+    $sessions.set(sessionRows)
+
+    renderSidebar('/', 'chat')
+
+    expect(screen.getByText('Sessions')).toBeTruthy()
+    expect(screen.queryByText('Projects')).toBeNull()
+  })
+})
+
 describe('ChatSidebar messaging owners', () => {
   const telegram = (id: string, profile: string, last_active: number) =>
     makeSessionInfo({ connection_id: 'local', id, last_active, profile, source: 'telegram', title: id })

apps/desktop/src/app/chat/sidebar/index.tsx

@@ -1266,11 +1266,21 @@ export function ChatSidebar({
     [projectModel, syncProjectCwd]
   )
 
-  // The Sessions section is a project switcher in grouped mode: its label reads
-  // "Sessions" when flat, "Projects" at the overview, and the project's name
-  // once you've entered one.
+  // The section header must name what the section is showing. Grouped mode
+  // reads "Projects" only while there IS a project switcher to show: a real
+  // project row, or a tree still resolving (the loading state keeps the label
+  // stable instead of flapping to "Sessions" and back). The synthetic Home
+  // bucket alone is just the flat session list wearing a project costume —
+  // with no real projects the section lists plain chat sessions, so it keeps
+  // the "Sessions" label (#62537).
+  const hasProjectRows = projectModel.some(node => !node.isNoProject)
+
   const sessionsLabel =
-    inProject && enteredProject ? enteredProject.label : worktreeGroupingActive ? s.projects.sectionLabel : s.sessions
+    inProject && enteredProject
+      ? enteredProject.label
+      : worktreeGroupingActive && (hasProjectRows || projectTreeLoading)
+        ? s.projects.sectionLabel
+        : s.sessions
 
   // Mirror the section's skeleton gate (projectsLoading + nothing to show yet):
   // while the skeleton is up there's no point also spinning the header count.