With the release of iOS 15 and its new notification management options, the Garmin Venu (and presumably all Garmin smartwatches with notification capabilities) does not properly support them.
Focus mode
All focus modes are handled as Do Not Disturb was handled on iOS14 and earlier. No notifications notify on the watch, even though they are configured as allowed apps and contacts within the focus mode's settings and notify on the phone as expected.
Notification summaries
When notification summaries are enabled, all notifications still notify on the watch in real-time even though they do not on the phone.
Overall
It seems likely that these are iOS limitations that Garmin can't work around, just like being able to choose which apps notify on the watch is available on Android but not iOS.
But truthfully, that's really all I want so I can have only a select few apps buzz my wrist. I know iOS doesn't support filtering which notifications are sent to the device, but it seems feasible that Garmin could solve this by filtering on-device. In this scenario, all notifications would still be sent to the watch but the watch would choose which to display.