Network problems are impeding the installation of the wireless HP M110w printer, according to an HP support agent, who is asking to pay $200 to fix them. Any suggestions to troubleshoot this issue? (My Mac Mini M4 is up to date, and I don't see any other problem)

If I had just bought that HP LaserJet M110w printer, I’d consider returning it for a refund.

(You’re being offered a fee larger than the selling price of that printer. Though whether that was HP or some third-party? If you do decide to return it, I’d suggest a Brother printer, though there are other choices.)

If you wish to persist with that HP printer, there is firmware from April. Confirm that the latest printer firmware is loaded, if you can get the printer to connect to Wi-Fi.

That HP printer supports AirPrint, which means it should work from all Apple devices, once connected to the Wi-Fi, and its firmware updated. This with no HP drivers installed.