This doesn't help helpless111 as it is for airplay printers. But others struggling with Sonoma 14 and HP printers in general might find it helpful.
After upgrading from 13.x to 14.1 my printer in the dock became a large "?". It was still in the list of printer but wasn't working correctly. For starters it would not scan. So I removed it and tried to install it again with the result that I could select the printer but not a driver. After a bit of searching I and (randomly clicking???) I got my printer to work.
possible requirement: HP printer capable of airprint , bonjour on (assumption is that you have bonjour on already since the printer worked before in macos 13 or less)
These are the steps I took
1) on macos: remove printer
(I did the next step because of a search result on getting scanning to work after a 'could not connect error'. it may not be necessary becasue under macos 13 it was on with ipv4 & 6)
2) on the HP printer: (via the internal webserver), change network | general | network protocols to ipv4 only
3) on macos: Add printer -> install ip printer (the basketball/earth icon at the top of add printer page) with ip address of the printer (192.168....etc or whatever you local printer ip is) and protocol AirPrint.
4) check you can print, you probably cannot scan (scanner connection error / or just nothing)
5) on macos: remove the printer
6) on macos: add printer - it should now be in the list and this time the driver should automatically come up.
result is that it now installs the HP printer with the airplay driver and that the scanning function works.
The effective difference after this success between macos 13.x and 14.x is that in the dock I no longer have the specific printer but instead have "print centre" (or what ever the spelling is of your MacOS language). Printer center (or centre) shows a list of all print devices but is effectively the same for me when it comes to the HP printer.
On reflection, considering the steps I took, it seems to me to be a bug in macos 14 since I got it to work without installing any HP software and just the 'out-of-the-box' drivers. If macos 14.1 was working correctly only step 6 would be needed. Especially step 3 seems to me like it gives macos 14.1 a kick in the right direction.