I discovered this question while searching for something else, but had just developed a solution for my own use in Debian. I think it answers the OP's question:
How to identify the way that a Debian (or another Linux distro) system use to configure its network stack?
 This is a rather simple-minded answer I think. It assumes that the software being used to manage the network runs as a service under systemd, and so amounts to listing all systemd units, and applying grep filters:
$ string1=$(systemctl list-units --all | grep -Ei 'networking\.|NetworkManager\.|networkd\.' | grep 'service' | grep -E 'running')  
$ string2=$(systemctl list-units --all | grep -Ei 'networking\.|NetworkManager\.|networkd\.' | grep 'service' | grep -Ev 'dead')  
$ if [ -n "$string1" ]; then echo ${string1::24}; else echo ${string2::20}; fi 
 As it turns out - for the versions of Debian 'bookworm' that I use at least, there are only 3 network services to choose from. (Netplan isn't installed, but could probably be accommodated under this scheme.) :
Note that Netplan isn't installed in my default installation, but could probably be accommodated under this scheme.
- NetworkManager.service
- systemd-networkd.service
- networking.service
 If you list those services, you see the following as the default setup (using NetworkManager) :
$ systemctl list-units --all | grep -Ei 'networking\.|NetworkManager\.|networkd\.' | grep 'service'  
  networking.service                     loaded    active   exited    Raise network interfaces
  NetworkManager.service                 loaded    active   running   Network Manager
  systemd-networkd.service               loaded    inactive dead      Network Configuration
 However, if you disable & mask NetworkManager in favor of ifupdown/networking.service, you will see the following. Note that the networking.service status does not change. :
$ systemctl list-units --all | grep -Ei 'networking\.|NetworkManager\.|networkd\.' | grep 'service' 
  networking.service                     loaded    active   exited    Raise network interfaces
  NetworkManager.service                 masked    inactive dead      NetworkManager.service
  systemd-networkd.service               loaded    inactive dead      Network Configuration
 
                