I see you've found an answer, so this is just FYI:
The people who run the RPi manufacturing operation decided to replace
nmcli as the default DHCP client program for the bookworm release. However, as I understand it,
dhcpcd remains in the distribution (or certainly available for the price of a
sudo apt install dhcpcd), so you can continue to use it - at least for a while.
And since this is an "FYI" kind of answer, I'll opine that
dhcpcd is a pretty good DHCP client. It's still actively maintained by Roy Marples, and recently upgraded to ver 10. I feel that part of the reason that
dhcpcd fell out of favor with the RPi manufacturing consortium was that they (and Debian) let it languish... they decided to stick with version 8 instead of following the upstream releases. Why?... I don't know, you'll have to ask them.
If you decide you do want to stick with
dhcpcd, you have a couple of options:
Stick with the old-ish version 8.1.2.
If you want the latest version (ver 10) you'll need to build it from source.
Finally, wrt to your comment, "I'm starting to wonder whether the Pi 5 been set up correctly.". Yeah - you're not alone. :)