Run some API operations in a background context. This should prevent some
of the SQLite "interrupted" errors, as those can occur when the context
closes while a query is running.
The API operations that Workers use are now mostly running in a separate
background context, at least from the moment onward when they can run
independently of the Worker connection.
Move the code related to task updates from workers to
`worker_task_updates.go`. It's going to get more complex with the
blocklisting in there; this prepares for that.
No functional changes.
