refactor: share sqlite open/with_conn helpers in db.rs

Converge the duplicated open_db (open + busy_timeout) and the
spawn_blocking + expect ceremony that every table access repeated
into one db.rs module. ChatStore no longer creates the tasks table
(schema ownership: queue.rs owns tasks, state.rs chat_state,
link_cache.rs link_cache). No schema or behavior change - all
CREATE TABLE statements are byte-identical, IF NOT EXISTS stays
idempotent, so existing data/task_queue.db files need no migration.

crates/xmedia-bot/src/db.rs

@@ -0,0 +1,37 @@
+//! Shared SQLite plumbing for the three tables in `data/task_queue.db`
+//! (`tasks` in queue.rs, `chat_state` in state.rs, `link_cache` in
+//! link_cache.rs).
+//!
+//! Every operation opens its own short-lived connection with a busy timeout:
+//! handler tasks enqueue while workers lease/update rows concurrently, and
+//! without the timeout a concurrent write fails immediately with SQLITE_BUSY
+//! and the operation is lost. All I/O runs inside `spawn_blocking` via
+//! [`with_conn`] — rusqlite connections are not Send-friendly to hold across
+//! an await point, and blocking the async executor stalls every handler.
+
+use rusqlite::Connection;
+use std::time::Duration;
+
+/// Opens the shared DB with a busy timeout.
+pub fn open_db(path: &str) -> rusqlite::Result<Connection> {
+    let conn = Connection::open(path)?;
+    conn.busy_timeout(Duration::from_secs(5))?;
+    Ok(conn)
+}
+
+/// Runs `f` against a fresh connection on a blocking thread, returning the
+/// closure's result. Owns the `spawn_blocking` + `expect` ceremony shared by
+/// every table access; the caller maps errors to its own log line.
+pub async fn with_conn<T, F>(path: &str, f: F) -> rusqlite::Result<T>
+where
+    T: Send + 'static,
+    F: FnOnce(&mut Connection) -> rusqlite::Result<T> + Send + 'static,
+{
+    let path = path.to_string();
+    tokio::task::spawn_blocking(move || {
+        let mut conn = open_db(&path)?;
+        f(&mut conn)
+    })
+    .await
+    .expect("db worker panicked")
+}