Add game start functionality with automatic player chip generation

Implemented host-controlled game start mechanism that generates unique player chips from user names. Added `started_at` timestamp to games and new `game_chips` table to store player identifiers. Chips are created using first name initial plus first two surname letters (e.g., SNE for Sascha Nesterovic) with automatic conflict resolution. Updated frontend to display start button for hosts, show game status, and populate chip selection modal

README.md

@@ -8,6 +8,8 @@ A small multiplayer web app that acts as a digital note sheet for a Harry Potter
 - Admin-managed user creation and deactivation
 - Multiple games per user
 - Join games using a short join code
+- Host-controlled game start with automatic player chips
+- Player chips are generated from the first name initial and first two surname letters, e.g. `SNE` for Sascha Nesterovic
 - Automatic player list with host indication
 - Personal note sheet for each player and game
 - Categories for suspects, items, and locations
@@ -200,6 +202,8 @@ The setup endpoint is available only while no administrator exists. After the fi
 - `GET /games/{game_id}`
 - `GET /games/{game_id}/members`
 - `PATCH /games/{game_id}/winner`
+- `POST /games/{game_id}/start`
+- `GET /games/{game_id}/chips`
 - `GET /games/{game_id}/sheet`
 - `PATCH /games/{game_id}/sheet/{entry_id}`