The HP OfficeJet Pro 9012e All-In-One Printer is an AirPrint-enabled device: About AirPrint - Apple Support.
Apparently HP had you install some kind of driver for that printer, but it was never necessary to do that. All that may be required is to add that printer to Printers & Scanners as an AirPrint device, if it is not already added as such.
As the dialog states and as Kurt Lang explained that extension (driver or whatever it happens to be) will cease to function at some future date as Apple continues to make macOS completely invulnerable to any kind of modifications whatsoever, even ones that you want, those that you authorize, including those released by legitimate developers with signed, notarized, Apple-approved code. It's the price we pay for vendors of utterly useless, arguably malicious junk people nevertheless insist upon installing on Macs.
There is nothing to authorize. It is merely informative. The reason for the dialog is that macOS makes no effort to determine what that software does, leaving that responsibility to the user. In your case you don't need to do anything, since that printer is already AirPrint-enabled and requires no such modifications to macOS for it to work.