refactor: convert from TypeScript to JavaScript with JSDoc

Author types in JSDoc comments. jsconfig.json keeps checkJs: true so
the editor's bundled TS server still validates them; CI can validate
with npx -p typescript tsc --noEmit on demand.

Renames (history preserved via git mv):
- next.config.ts        -> next.config.mjs
- app/layout.tsx        -> app/layout.jsx
- app/page.tsx          -> app/page.jsx
- app/master/page.tsx   -> app/master/page.jsx
- components/player-board.tsx -> components/player-board.jsx
- lib/game-logic.ts     -> lib/game-logic.js
- tsconfig.json         -> jsconfig.json (same @/* alias)

Drops typescript and @types/node, @types/react, @types/react-dom
from devDependencies. Removes vendored next-env.d.ts. eslint config
no longer pulls in eslint-config-next/typescript.

Behavior unchanged. Build, lint, and dev profiles verified.

web/package.json

@@ -16,12 +16,8 @@
   },
   "devDependencies": {
     "@tailwindcss/postcss": "^4",
-    "@types/node": "^20",
-    "@types/react": "^19",
-    "@types/react-dom": "^19",
     "eslint": "^9",
     "eslint-config-next": "16.2.2",
-    "tailwindcss": "^4",
-    "typescript": "^5"
+    "tailwindcss": "^4"
   }
 }