After the first sync, Context syncs automatically in the background. You don't need to open the app to keep data flowing.
Your first sync is the slow one, because it's backfilling all the history already on your device. Everything after that only handles what's new.
To check when your data last updated: open Settings by tapping your profile in the top right of the app. The last sync time is shown there.
To check what actually arrived: the fulcra data-updates command reports everything that landed over a period you choose. Note that it filters on when data arrived, not when it happened, so last night's sleep typically arrives this morning and a check covering the last day will include it. https://docs.fulcradynamics.com/cli/#data-updates

