if you connected the cable between the printer and the PC before you had installed the drivers, the printer would not mount as a device. In fact, it would never connect to that PC ever again. Apparently, it ruined the registry until you reformatted and reinstalled the OS.

Don't take this as a defense of HP... but it's a known behavior of Windows where once it associates a device with some driver, like the default ones which didn't work for that printer, it won't try to search for new drivers again... until the device is removed from the system.

There are several ways of doing that, this is a modern writeup:

https://www.computerworld.com/article/3322513/how-to-reduce-windows-driver-bloat-remove-outdated-drivers.html

Back in the day, there were several different ways:

• Go into Device Admin, click on show hidden devices, and remove the wrongly detected printer.
• Use... I don't recall the name right now, but there is a tiny tool that allows you to remove unused devices, handily sorted by "last used" date.
• Use any of several tools that allow you doing the same, including some PowerShell commands.

You didn't need to reinstall.