Update it from your Plugins screen like any other WordPress plugin. That is the whole thing.
Your connection keeps working. You do not need to download anything, reconnect, or sign in again. The connection address never changes, so an update cannot break it.
Two things worth knowing:
- WordPress checks for plugin updates on a schedule, so a new version can take a few hours to show on your Plugins screen. Dashboard → Updates checks straight away.
- If your site allows automatic plugin updates, WordPress for Cowork updates itself.
If you ever want to check what changed, the changelog lists every release.