That sounds pretty bad and probably means other things are broken too. The easiest option would probably be a reinstall at this point, but if you want to learn something you can also try to salvage your install.

To recover, it's probably easiest to manually configure your Ethernet connection as described by InnerScientist and then re-install the network-manager package.

You can check the status of the network-manager package using dpgk. It should look like this (ii at the start, but it sounds like it's not installed in your case):

$ dpkg -l | grep -i network-manager
ii  network-manager                         1.52.1-1                        amd64        network management framework (daemon and userspace tools)
ii  network-manager-l10n                    1.52.1-1                        all          network management framework (translation files)

You can also check /var/log/apt/history.log to see what went wrong and if there are other things you need to fix.

I performed the upgrade in two steps apt upgrade --without-new-pkgs and apt full-upgrade (based on the release notes). I can see the following on the line Upgrade: for the command apt full-upgrade:

network-manager:amd64 (1.42.4-1+deb12u1, 1.52.1-1)

On the Remove: line you can see the packages that were removed. Unfortunately, the names of many libraries were changed in this release (e.g., libreadline8:amd64 to libreadline8t64:amd64), so there's a lot of noise in there. Maybe you can look at that line and ignore everything that starts with lib to see if any other important packages were removed.