Just want to add my own experience with this. I'm in the same situation as Wearemode. I run a custom app for our business and have told our stores not to upgrade to Shopify POS 7 due to the lack of development support for the past month.
Currently on iOS 15.5, Shopify POS 7.0.5, and have tested my custom app using @Shopify/app-bridge version 2.0.24, 3.1.0, and the latest 3.1.1.
What I've found so far is that first, the process name for Shopify POS seems to have changed. It is no longer "Shopify POS," it is now "POSNext," so the documentation is out of date. Second, there is no longer a subsystem called "App Bridge Debugging," or at least in my experience, it does not show up at all in the Mac Console app as it used to with Shopify POS 6.
There is no console feedback regardless of which version of @Shopify/app-bridge is used, and tested with 7.0.0 - 7.0.5.