Never been a problem with that, do you have any links to show that people who bought computers (not built) had reinstallation issues? I've reinstalled windows and helped others countless times on their Lenovos, Dells, and yes even my HP machines. Windows 10 and 11 doesn't even prompt you for any activation codes, its built into the bios, so all you do is reinstall the os
I tend to agree with Maflynn. Activation is linked to the hardware so activation will not be an issue with the same version of windows like home or Pro. You just won't have an activation issue. I have re-installed windows by completely wiping the drive and using a general windows iso direct from microsoft and most everything works and there is no issue with activation.
What can be tricky is getting all the drivers for specific hardware tied to a device. This is much less of a problem with a desktop than a laptop though. Generally speaking from a laptop you can go to HP website and download a driver you need specific to your device from HP by entering your serial number. It can be a bit of a process and for general users this could be confusing. That is my only bit of contention with the advise of getting a general iso bootable usb backup. However it is probably the only way to get a "clean" installation of windows without all the bloat.
I generally recommend that most general users get the specific bootable usb from their manufacturer(in this case HP) which they usually can request free of charge which will return their computer to the state it was when they bought it. Lenovo will allow you to download a device specific iso and has software that will create a recovery usb for you for example.
Just using a bootable usb based on a genral ISO from Microsoft can be tricky depending on the hardware and manufacturer and users level of knowledge in this area.
Generally speaking it is best to simply use the hardware specific version of Windows that came with your device and removing the bloatware by uninstalling it. You can also use registry changes to eliminate telemetry(this is a more advanced method and requires Windows Pro license). But this is the safest method and ensures your device will have all of the drivers needed and will continue to get updates from the manufacturer.