Thanks to the kind and competent help of @stephenw10 my box is working again: The packages available list is fully populated, branches are showing in the system update menu, and it is now fully up to date to 23.09.1.
For anybody appreciating closure: I think the root cause of my problem was an empty /usr/local/etc/pfSense/pkg/repos directory. I do not know how it became emptied out, but the cause of it not to be repopulated with all the commands mentioned above, was my Netgate Device ID (NID) no longer being registered. It also appeared to have changed.
I did add a network card to my box exactly a year ago, and took it out a week later, when it became unstable because it ran too hot. Two weeks ago I installed an alternative that does not run hot, and it is still in. I do know when my NID got invalidated, and if it reverts back to valid in between the to cards, but Stephen re-validated it again, and I will no longer change my box' configuration now. Ever.