Hi,
The HP OfficeJet Pro 9010 All-In-One Printer and HP ENVY 5530 e-All-In-One Printer series are listed in the October 26, 2022 US edition of About AirPrint - Apple Support. This means that both printers are supported by the driverless AirPrint technology, and can be used without additional drivers, provided that the printers and the Mac computer are connected to the same network (Wi-Fi router). An AirPrint-enabled printer is compatible with macOS 13 Ventura.
AirPrint works with wireless (Wi-Fi) or wired (Ethernet) network connections. Since the OfficeJet Pro 9010 has Ethernet, you could choose to wire it to one of the LAN ports of the Wi-Fi router instead of using a wireless printer connection.
Some HP printers need an HP Smart app for setup and ink-management purposes.
You may want to reset the printing system and re-add the printers. See the following articles:
Reset the printing system on your Mac to solve a problem – Apple Support (UK)
Add a printer to your printer list so you can use it on Mac – Apple Support (UK)
If there is a problem with AirPrint device discovery, you could try the following procedure (in this order, with these waiting times): Power off the Wi-Fi router, the printer(s), the Mac, and all other connected devices/computers. Wait two to three minutes. Power on the router. Wait two to three minutes. Power on the printer(s). Wait a minute or two. Power on the Mac. Finally, power on all other devices/computers