(To make a long story short: It did not work and then I decided to split the problem into 2: To try to print when the printer is connected via USB to the computer, and only when it works, to proceed to network installation).
USB - OK
I attempted to use the instructions provided here, but the printer did not print. Subsequently, I came across a video and modified the driver to hp LaserJet 1010 HB. Following this adjustment, I successfully printed from my Windows 11 Pro for Workstations computer.
Network
Using the same LaserJet 1010 HB driver, I attempted the network solution by connecting the printer to the USB port at the back of the router (Asus RT-AC87U). I followed the instructions provided here, but unfortunately, the document doesn't leave the queue and the printer doesn't print.
How to debug this case?
ASUS EZ printer sharing utility
on your Windows ?