perf(header): cap session tabs at 20; tooltip data loads on hover only

Auto-add means the strip only grows, so past 20 tabs the oldest one
leaves the working set (the newly opened tab is always the survivor).
The branch/worktree/PR/project subscriptions that feed the hover
tooltip moved into the tooltip body component, which mounts only while
the tooltip is open — a resting tab now subscribes only to its status
dot's session status and unread count.

packages/ui/src/stores/useSessionTabsStore.test.ts

@@ -32,6 +32,15 @@ describe('useSessionTabsStore', () => {
     expect(useSessionTabsStore.getState().tabIds).toBe(before);
   });
 
+  test('caps the working set at 20, evicting the oldest tab', () => {
+    useSessionTabsStore.setState({ tabIds: Array.from({ length: 20 }, (_, i) => `s${i}`) });
+    useSessionTabsStore.getState().ensureTab('s-new');
+    const ids = useSessionTabsStore.getState().tabIds;
+    expect(ids).toHaveLength(20);
+    expect(ids[0]).toBe('s1');
+    expect(ids.at(-1)).toBe('s-new');
+  });
+
   test('removeTabs drops only confirmed-gone ids and no-ops otherwise', () => {
     useSessionTabsStore.setState({ tabIds: ['a', 'b'] });
     const before = useSessionTabsStore.getState().tabIds;

packages/ui/src/stores/useSessionTabsStore.ts

@@ -24,6 +24,8 @@ interface SessionTabsStore {
   removeTabs: (sessionIds: readonly string[]) => void;
 }
 
+const MAX_SESSION_TABS = 20;
+
 type PersistedSessionTabs = { tabIds: string[] };
 
 export const useSessionTabsStore = create<SessionTabsStore>()(
@@ -36,7 +38,11 @@ export const useSessionTabsStore = create<SessionTabsStore>()(
           if (!sessionId) return;
           const { tabIds } = get();
           if (tabIds.includes(sessionId)) return;
-          set({ tabIds: [...tabIds, sessionId] });
+          // Soft cap: with auto-add the strip only ever grows, so past the cap
+          // the oldest tab (never the one being opened, which lands last)
+          // leaves the working set.
+          const next = [...tabIds, sessionId];
+          set({ tabIds: next.length > MAX_SESSION_TABS ? next.slice(next.length - MAX_SESSION_TABS) : next });
         },
 
         closeTab: (sessionId) => {