Static IP is the best option. Set the IP on the printer itself, and also reserve that IP number in your router to make sure it's always available for your printer only and no other device.
The v3 and v4 "universal" drivers are garbage. The latest version that I could find that is fully functional is 2012 for the PCL3 raster driver for my 24 inch Z3200PS Rev B model. The driver is available on the HP website, but you need to select an old OS version like Windows 8 to find it. Don't worry about that, it still works fine with Win 10 and I hear Win 11 as well.
HP Utility 1.17.0.3 also works fine.
Completely remove / uninstall the printer driver package. You can leave HP Utility installed, it's separate. Also use Windows Printer Management to remove any ports that were created for the Z3200. After it's "clean" and rebooted you can install the 2012 driver package.
When done you can check the advanced printer properties in Windows to verify that the Bidirectional Communications option is checked. If it's not or it's greyed out then you still have a problem with your installation.