feat(app): detect prior server activity for layout transition

packages/app/src/context/server.tsx

@@ -12,6 +12,7 @@ type ServerProjectState = {
   lastProject: Record<string, string>
   recentlyClosed: Record<string, string[]>
 }
+type PersistedServerState = ServerProjectState & { list: StoredServer[] }
 const HEALTH_POLL_INTERVAL_MS = 10_000
 // The store retains more history than is displayed. Consumers filter recently closed entries
 // against the live project list (dropping deleted projects) and then cap the visible count via
@@ -178,6 +179,13 @@ export function resolveServerList(input: {
   return [...deduped.values()]
 }
 
+export function hasPersistedServerData(store: PersistedServerState) {
+  if (store.list.length > 0) return true
+  if (Object.values(store.projects).some((projects) => projects.length > 0)) return true
+  if (Object.values(store.lastProject).some(Boolean)) return true
+  return Object.values(store.recentlyClosed).some((projects) => projects.length > 0)
+}
+
 export namespace ServerConnection {
   type Base = { displayName?: string; label?: string }
 
@@ -331,10 +339,12 @@ export const { use: useServer, provider: ServerProvider } = createSimpleContext(
       () => allServers().find((s) => ServerConnection.key(s) === state.active) ?? allServers()[0],
     )
     const isLocal = createMemo(() => ServerConnection.local(current()))
+    const hasPersistedData = createMemo(() => hasPersistedServerData(store))
 
     return {
       ready: isReady,
       isLocal,
+      hasPersistedData,
       get key() {
         return state.active
       },