Add alpha session gate with cookie auth and login UI.

docs/protocol.md

@@ -25,9 +25,48 @@ closes connections whose hello carries a different version with `1002 ProtocolEr
 
 ## HTTP API
 
+Most routes require a signed session cookie set by `POST /api/session`. Without it the server
+returns `401`. Public exceptions: `GET /health` and the three `/api/session` routes.
+
 Game dates are ISO-8601 UTC instants. The in-game calendar has no time zone — UTC is only used so
 the wire format is unambiguous, and the client formats it back in UTC.
 
+### `POST /api/session`
+
+Alpha login. Body:
+
+```json
+{ "password": "alpha", "userName": "Leo" }
+```
+
+Success (`200`) sets an HttpOnly cookie (`SameSite=Lax`, `Path=/`) and returns:
+
+```json
+{ "userName": "Leo" }
+```
+
+The name is normalized like a school name (trim, no control characters, 1–40 chars). Occupancy is
+case-insensitive: `Leo` and `leo` are the same person; the first spelling is kept in
+`saves/users.json`.
+
+| Status | `code` | When |
+| --- | --- | --- |
+| `401` | `bad-password` | Wrong alpha password |
+| `400` | `invalid-name` | Name fails normalization |
+| `409` | `name-online` | A live WebSocket already uses that name |
+
+### `GET /api/session`
+
+Returns `{ "userName": "Leo" }` when the cookie is valid, otherwise `401`.
+
+### `DELETE /api/session`
+
+Clears the session cookie. `204`.
+
+The WebSocket at `/ws/game` uses the same cookie on upgrade. Without a valid cookie the server
+closes the connection with a policy violation and never sends Welcome. Hello is unchanged
+(version + locale only).
+
 ### `GET /api/schools`
 
 Everything the main menu needs in one request. `schoolWeekDays` is 5–7 working days counted