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/tsconfig.json

@@ -11,12 +11,12 @@
     "declaration": false,
     "sourceMap": true,
     "outDir": "./dist",
-    "rootDir": ".",
     "baseUrl": ".",
     "lib": ["ES2022", "DOM"],
     "paths": {
       "@soak/*": ["./*"],
-      "@bot/*": ["../e2e/bot/*"]
+      "@bot/*": ["../e2e/bot/*"],
+      "@playwright/test": ["./node_modules/@playwright/test"]
     }
   },
   "include": ["**/*.ts"],