feat(soak): SessionPool — seed, login, acquire contexts

Owns BrowserContexts, seeds via POST /api/auth/register with the
invite code on cold start, warm-starts via localStorage injection of
the cached JWT, falls back to POST /api/auth/login if the token is
rejected. Exposes acquire(n) for scenarios.

Infrastructure changes needed to import the real GolfBot class from
tests/e2e/bot/ without the Task-10 structural-interface workaround:
 - Add @playwright/test as devDep so value-imports in e2e/bot/*.ts
   resolve at runtime (Page/Locator/expect are pulled even as types)
 - Remove rootDir from tsconfig so TS follows cross-package imports;
   add a paths entry so TS can resolve @playwright/test from the soak
   package's node_modules when compiling files under tests/e2e/bot
 - Drop the local GolfBot structural interface + its placeholder
   GamePhase/StartGameOptions/TurnResult types; re-export the real
   class from types.ts

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

tests/soak/package.json

@@ -16,6 +16,7 @@
     "ws": "^8.16.0"
   },
   "devDependencies": {
+    "@playwright/test": "^1.40.0",
     "tsx": "^4.7.0",
     "@types/ws": "^8.5.0",
     "@types/node": "^20.10.0",