feat(v0.6): add Home (⌂) button to reach Sessions/Projects from a session

Once a project/session tab was open, the home chooser (Sessions/Projects
segmented control) was hidden and only reachable by closing every tab — no
way back to the Projects view to open another project.

Add a ⌂ Home button to the tab bar that overlays the chooser on top of the
open tabs (homeForced flag; updateHomeView shows home when no tab OR forced,
hiding the terminal panes). Clicking ⌂ again, clicking a tab (activate resets
homeForced), or opening another session/project dismisses the overlay.
Closing the last tab resets the flag. The button highlights while active.

Tests: +3 (tabs.test.ts). Full suite 415 green; both typechecks clean;
verified in-browser (open tab → ⌂ → Projects panel reachable → ⌂ → terminal).

test/tabs.test.ts

@@ -463,3 +463,51 @@ describe('TabApp — P6 openProject + home segmented control', () => {
     expect(app.snapshot()[0]!.title).toBe('bare-repo')
   })
 })
+
+describe('TabApp — Home (⌂) button: reach the chooser from an open session', () => {
+  it('overlays the home chooser over an open tab, then toggles back', () => {
+    const { paneHost, tabBar } = makeHosts()
+    const app = new TabApp(paneHost, tabBar)
+    app.newTab()
+    const seg = paneHost.querySelector('.home-seg') as HTMLElement
+    const homeBtn = tabBar.querySelector('.tab-home') as HTMLButtonElement
+    expect(homeBtn).not.toBeNull()
+    expect(seg.style.display).toBe('none') // terminal owns the screen
+
+    homeBtn.click() // overlay the home chooser
+    expect(seg.style.display).toBe('flex')
+    expect(launcherVisible.value).toBe(true) // default sessions view
+    expect(homeBtn.classList.contains('active')).toBe(true)
+
+    homeBtn.click() // back to the terminal
+    expect(seg.style.display).toBe('none')
+    expect(launcherVisible.value).toBe(false)
+    expect(homeBtn.classList.contains('active')).toBe(false)
+  })
+
+  it('can switch to Projects from the overlay and open another project', () => {
+    const { paneHost, tabBar } = makeHosts()
+    const app = new TabApp(paneHost, tabBar)
+    app.openProject('/p/one', 'one')
+
+    ;(tabBar.querySelector('.tab-home') as HTMLButtonElement).click() // overlay home
+    ;(paneHost.querySelectorAll('.home-seg-btn')[1] as HTMLButtonElement).click() // Projects
+    expect(projectsVisible.value).toBe(true)
+
+    app.openProject('/p/two', 'two') // opening dismisses the overlay
+    expect(app.snapshot()).toHaveLength(2)
+    const seg = paneHost.querySelector('.home-seg') as HTMLElement
+    expect(seg.style.display).toBe('none')
+    expect(projectsVisible.value).toBe(false)
+    expect((tabBar.querySelector('.tab-home') as HTMLButtonElement).classList.contains('active')).toBe(false)
+  })
+
+  it('⌂ is a no-op when no tab is open (home already shown)', () => {
+    const { paneHost, tabBar } = makeHosts()
+    new TabApp(paneHost, tabBar)
+    const seg = paneHost.querySelector('.home-seg') as HTMLElement
+    expect(seg.style.display).toBe('flex')
+    ;(tabBar.querySelector('.tab-home') as HTMLButtonElement).click()
+    expect(seg.style.display).toBe('flex') // still shown, no crash
+  })
+})