I spent over 30 years doing computer support, that included iPhones from way back.
No this is not an error with my printer (not really), one things and only one thing changed in my setup, I updated my phone to the latest iOS. Now it is possible that Apple make a change to Air Print, but in doing the change they missed some thing for backwards compatibility. Yes it is possible that there is a change in AirPrint that can be made on the printer, no there is not an update available at this time for my printer (Dell E525W). The printer is 5 to 10 years old, the most current firmware was designed around the current AirPrint specification at that time. No I do not have any VPN on my phone. Yes private WiFi address is enabled, but it worked with this before the iOS 17 update, (I disabled it and tested, no joy). Yes the phone, network equipment, and printer have been power cycled.
This is an iOS 17 update issue, Apple made some minor change in AirPrint that had disrupted connections to older printers, not all printers but some older printer. The symptoms are that when you go to printer, you select the printer, the printer is seen by your phone, it is listed as an available printer (is broadcasting that is it an AirPrint printer), when it is selected the phone returns to the print screen but in the selected printer field it still says "no printer selected".
Now it is possible there is a setting that can be changed in the AirPrint Settings on the printer that will fix this. But the bottom line is this all worked before iOS 17 and fails after iOS 17. If it is an AirPrint setting on the printer, why hasn't Apple released this setting information. What bothers me is I have not see Apple replay to this issue, it is being reported by many people, they should tells us they recognize the issue and are looking into it. They can tell me they made a change to AirPrint and printer manufactures need to release and update. They can tell us something, nope crickets.