Battleship Overall Game Stats

## Description

Log and save Battleship game stats to a database.

### Requirements

- Log games played, shots taken, misses, hits, and ships sunk.
- Create a home page widget for the global stats.
- Hide widget if errors occur.
- Hide widget if rate limited.

Look for existing game logic and database setup in the monorepo. Identify where game events are emitted and where to insert logging. The home page widget likely connects to a stats API endpoint; check for existing React components and API routes. 'Done' means stats are saved, an endpoint serves them, and a widget displays them conditionally.

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