Not sure if this is a bedrock issue, or a composer one, or something else. Basically on my admin pages for my sites I do not see when any plugin updates are available. I do my updates via composer and that all works fine, but I usually just glance at the backend to see if any updates have been released. In my development site (trellis) it works fine, but on my staging and production sites I do not see any update messages. Before I really dig into figuring it out I want to make sure this is not some behavior associated with disabling auto updates or some other configuration setting in Bedrock.
I also have disabled WP-Cron and running a linux cron task as suggested. It looks like this:
*/5 * * * * curl https://STAGINGSERVER/wp/wp-cron.php > /dev/null 2>&1
Looks okay to me but maybe it is not kicking off the update check?