refactor: centralize relay state into zustand store, deduplicate playwright client maps

Introduce relay-state.ts with a single Zustand vanilla store holding all relay
server state (extensions, playwright clients, targets). All state transitions are
pure functions: data in, data out, no I/O inside setState().

Key changes:
- Move scattered mutable Maps (extensionConnections, extensionKeyIndex,
  playwrightClients) into one RelayState atom managed by zustand/vanilla
- Co-locate I/O handles (ws, pingInterval, pendingRequests) on ExtensionEntry
  instead of separate Maps, following the same pattern for PlaywrightClient
- Merge PlaywrightClientState + PlaywrightClientIO into single PlaywrightClient
  type with { id, extensionId, ws } — eliminates the duplicate playwrightClientIO
  map that had to stay in sync (and was already buggy: removeClientsForExtension
  only cleaned playwrightClients but leaked playwrightClientIO entries)
- Derive extensionKeyIndex on demand via findExtensionByStableKey() linear scan
  instead of maintaining a separate index Map
- Add relay-state.test.ts with 38 pure data-in/data-out tests covering all
  state transitions and derivation helpers

pnpm-lock.yaml

@@ -362,6 +362,9 @@ importers:
       zod:
         specifier: ^4.3.5
         version: 4.3.5
+      zustand:
+        specifier: ^5.0.8
+        version: 5.0.8(@types/react@19.2.7)(react@19.2.3)
     devDependencies:
       '@browserbasehq/stagehand':
         specifier: ^3.0.5
@@ -9493,6 +9496,14 @@ snapshots:
     optionalDependencies:
       vite: 7.3.0(@types/node@25.0.3)(jiti@2.6.1)(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0)
 
+  '@vitest/mocker@4.0.8(vite@7.2.2(@types/node@24.10.1)(jiti@2.6.1)(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0))':
+    dependencies:
+      '@vitest/spy': 4.0.8
+      estree-walker: 3.0.3
+      magic-string: 0.30.21
+    optionalDependencies:
+      vite: 7.2.2(@types/node@24.10.1)(jiti@2.6.1)(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0)
+
   '@vitest/mocker@4.0.8(vite@7.2.2(@types/node@25.2.0)(jiti@2.6.1)(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0))':
     dependencies:
       '@vitest/spy': 4.0.8
@@ -9544,7 +9555,7 @@ snapshots:
       sirv: 3.0.2
       tinyglobby: 0.2.15
       tinyrainbow: 3.0.3
-      vitest: 4.0.8(@types/node@25.2.0)(@vitest/ui@4.0.8)(jiti@2.6.1)(jsdom@27.2.0(bufferutil@4.0.9))(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0)
+      vitest: 4.0.8(@types/node@24.10.1)(@vitest/ui@4.0.8)(jiti@2.6.1)(jsdom@27.2.0(bufferutil@4.0.9))(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0)
 
   '@vitest/utils@4.0.16':
     dependencies:
@@ -13580,7 +13591,7 @@ snapshots:
   vitest@4.0.8(@types/node@24.10.1)(@vitest/ui@4.0.8)(jiti@2.6.1)(jsdom@27.2.0(bufferutil@4.0.9))(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0):
     dependencies:
       '@vitest/expect': 4.0.8
-      '@vitest/mocker': 4.0.8(vite@7.2.2(@types/node@25.2.0)(jiti@2.6.1)(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0))
+      '@vitest/mocker': 4.0.8(vite@7.2.2(@types/node@24.10.1)(jiti@2.6.1)(lightningcss@1.31.1)(tsx@4.20.6)(yaml@2.6.0))
       '@vitest/pretty-format': 4.0.8
       '@vitest/runner': 4.0.8
       '@vitest/snapshot': 4.0.8