Deleted you put me on the right track:
it requires that all network interfaces have an IPv4 that is not APIPA
I configured all network interfaces with a valid IP address, and then finally the network settings deployment got past that 1% block.
However, apart from NOT BEING DOCUMENTED ANYWHERE, this is a completely crazy requirement: the whole purpose of this procedure is to configure network interfaces, it's simply absurd to require them to be already configured in order to overwrite their configuration (also, some of the interfaces are just not meant to have an IP address in the first place).
Let's just consider this another macroscopic bug that needs to be fixed.
Now, it would be really nice if Microsoft started actually fixing all those bugs that plague Windows Admin Center...