While it is true that the HP Smart for Desktop app
(https://apps.apple.com/us/app/hp-smart-for-desktop/id1474276998?mt=12)
appears to require macOS 12 or later, you may want to investigate whether a workaround possibly would allow use of macOS 10.15 Catalina with this printer.
First of all, AirPrint is mentioned in the specifications for the HP Smart Tank 7000 series:
https://support.hp.com/us-en/product/product-specs/hp-smart-tank-7000-series/model/2100178735
(HP Smart Tank 7001, 7002, 7005, and 7006 models are listed as supported in About AirPrint - Apple Support en-us edition February 12, 2025).
Generally speaking, an AirPrint printer can be used without additional drivers/software when connected to the same network (Wi-Fi router) as a Mac computer running macOS 10.15 Catalina.
A printer manufacturer may provide software for setup, ink management and similar purposes. Such software may not be absolutely necessary, but could be a requirement in cases where an ink subscription agreement has been signed.
If a requirement exists for certain (setup, et cetera) steps, have you checked whether the HP Smart app for iPhone or iPad could be used instead?
https://apps.apple.com/us/app/hp-smart/id469284907
Alternatively, if necessary, an Android version?
https://play.google.com/store/apps/details?id=com.hp.printercontrol&hl=en-US