Complete change of hardware

Will my current Ubuntu 20.04.2 LTS work on a completely new system (new hardware) if i simply plug in my old HDD into the new system?

As far as I know, the drivers are in the kernel which is what makes the OS most stable and hence there is no need for installation of drivers. The OS usually works fine on any system/hardware that is around a year old.

It might / it can.

I recently moved a hard drive with a 18.04 Ubuntu MATE installation from an old HP laptop to an even older Dell laptop.

It worked seamlessly, but these were simple machines without dedicated graphics cards, your mileage may vary.

with some preparations it can work. (I made it for some years).

I would search which closed sources driver or firmware you need on your new hardware and install it on your old hardware.

then I would to remove closed source drivers (like nvidia or for wlan cards) which was needed on your old system but not on your new hardware.

and a backup is not a bad Idea; also to have a bootable usb-stick/DVD

sorry I'm not good in explaning in english.