fix: reuse database connection in server state

[echobt]

This PR fixes a performance issue where a new database connection was created for every request. By reusing the database connection stored in the server state, we reduce file descriptor usage and avoid potential SQLITE_BUSY errors under load.

Changes:

• Added db: Mutex<Database> to ServerState.
• Initialized the database connection once during server startup.
• Updated request handlers to lock and use the shared database connection instead of opening a new one.