fix(tui): load root sessions in session switcher (#33931)

Request root sessions before applying the session list limit so child
sessions cannot crowd roots out of the switcher.

Keep the synchronized cache available while requests are pending or fail,
reconcile results with live updates, and retain current and pinned sessions.
Preserve selection by session ID when asynchronous results reorder the list.

Closes #16270
Closes #32725

packages/tui/test/cli/cmd/tui/sync-fixture.tsx

@@ -6,6 +6,7 @@ import { KVProvider, useKV } from "../../../../src/context/kv"
 import { ProjectProvider, useProject } from "../../../../src/context/project"
 import { SDKProvider } from "../../../../src/context/sdk"
 import { SyncProvider, useSync } from "../../../../src/context/sync"
+import { ExitProvider } from "../../../../src/context/exit"
 import { createEventSource, createFetch, type FetchHandler, directory } from "../../../fixture/tui-sdk"
 import { TestTuiContexts } from "../../../fixture/tui-environment"
 export { createEventSource, createFetch, directory, eventSource, json, worktree } from "../../../fixture/tui-sdk"
@@ -48,9 +49,11 @@ export async function mount(override?: FetchHandler, state?: string) {
         <KVProvider>
           <SDKProvider url="http://test" directory={directory} fetch={calls.fetch} events={events.source}>
             <ProjectProvider>
-              <SyncProvider>
-                <Probe />
-              </SyncProvider>
+              <ExitProvider exit={() => {}}>
+                <SyncProvider>
+                  <Probe />
+                </SyncProvider>
+              </ExitProvider>
             </ProjectProvider>
           </SDKProvider>
         </KVProvider>

packages/tui/test/cli/cmd/tui/sync.test.tsx

@@ -25,6 +25,7 @@ describe("tui sync", () => {
 
     try {
       expect(kv.get("session_directory_filter_enabled", true)).toBe(true)
+      expect(session.at(-1)?.searchParams.get("roots")).toBeNull()
       expect(session.at(-1)?.searchParams.get("scope")).toBeNull()
       expect(session.at(-1)?.searchParams.get("path")).toBe("packages/tui")
 
@@ -33,6 +34,7 @@ describe("tui sync", () => {
 
       expect(session.at(-1)?.searchParams.get("scope")).toBe("project")
       expect(session.at(-1)?.searchParams.get("path")).toBeNull()
+      expect(session.at(-1)?.searchParams.get("roots")).toBeNull()
     } finally {
       app.renderer.destroy()
     }