.One data point other users might benefit from:

I recently had to move to a new PC. Had been using the no-longer-supported QB Desktop 2019, so was concerned whether I'd be able to move that to the new PC too.

I had bought that copy of QB from Amazon in 2019, and Amazon still had the original download available to me in my Orders history. That is, I didn't have to purchase it again, just re-download the original purchase and keep the same key.

I ran the installation, being careful not to accept any updates at all. It seems to be running just fine now, despite a one-time warning that my company file had been edited in a later version of QB. There are no prompts to log in! I can't use the Bank feeds any more (because 2019 is unsupported), but can limp along without that until I wind the company down and retire in a few years.