Hello Susan,
The HP OfficeJet Pro 8028 All-In-One Printer and HP OfficeJet Pro 8028e All-in One Printer are listed as supported models in About AirPrint - Apple Support (en-us edition, January 23, 2024). This should mean that they can be used without additional drivers/software, provided that they are connected to the same network (Wi-Fi router) as your Mac. AirPrint may in some cases be used with operating systems as low as Mac OS X 10.7 Lion.
However, a printer manufacturer may also provide special software with higher system requirements for setup, ink management and similar purposes. This could especially be the case if an ink subscription ageement is involved.
Would it be correct to assume that the use of HP Smart for Desktop (which requires macOS 11.0 Big Sur or later) has been recommended here? If so, printing ought to work anyway from the Mac just using AirPrint.
Add a printer on Mac – Apple Support (UK)
If HP Smart is absolutely necessary (for example, for ink management), you could perhaps try to set up the printer via an iPhone/iPad and the iOS/iPadOS app version.
https://apps.apple.com/us/app/hp-smart/id469284907
By the way, AirPrint works with wireless (Wi-Fi) or wired (Ethernet) network connections. If a printer has an Ethernet port, you could choose to wire it to one of the LAN ports of the Wi-Fi router (instead of using a wireless printer connection), if you so wish. Ethernet may be more stable, and some Wi-Fi-related difficulties could be avoided. The Mac could still access the printer wirelessly via the router, and the same would be true for an iPhone/iPad.