Open smart lock with Apple Watch (no attached iPhone -> Apple Family Setup)

Product name

Smart lock 3.0

Summary

I have set up an old Apple Watch LTE for my son via the Apple Family Setup and would like to allow him to open our Nuki 3.0 via Bluetooth.
Unfortunately, it doesn’t seem to be possible to install the Nuki app on the Apple Watch directly without being connected to an own iPhone.
Apparently it is also not enough to be connected to the same iCloud account as the Apple Watch via an iPad and install the Nuki app there. It seems that there has to be a connection to an iPhone.
Is there any way to get this to work directly on the watch without an iPhone?

In the meantime, the Nuki app is interestingly displayed on the Apple Watch, although the pairing was only done via Family Setup on the parent iPhone. Maybe installing the Nuki app on the child’s iPad has helped after all?
However, on the child’s Apple Watch it only says “no Nuki found”, so unfortunately the app still cannot be used.

Question might be a potential limitation regarding bluetooth protocol / version? The series 3 has bt 4.2 only. Not sure about the amount of data the Nuki retrieves.

It’s a Serie 5 LTE for the kid (a little bruised but was a good deal)