Yes you’re forced to upgrade each time a new MACOS version comes out, it doesn’t matter if it can run on the new OS version. It’s programmed to stop opening and ask you to pay to keep it working.
Citation needed, as they say.
I've been using Parallels more or less since it came out and a version is usually good for 2-3 MacOS versions. I've just upgraded to V15 from version 12 which was originally released for El Capitain, but was working with a few glitches (that didn't affect me) under Mojave. Yes, you get an 'ad' box when a new version comes out, but you can tell it to go away.
Its a hypervisor that needs to tie closely into both the host and guest operating system, so its no great surprise that it often breaks with major OS upgrades. Programmers need to eat hot meals and sleep indoors and you can't expect free upgrades for life for a single sub-$100 purchase. $40 every 2-3 years is hardly usury.
That said, Parallels don't help their case - you'd be forgiven from their advertising and reminder emails for thinking that you do need an upgrade for every Mac OS version, and they have an irritating habit of 'pushing' a cut-price upgrade offer a month or two before a new version comes out. The subscription price for the Pro version (with features that used to be part of the standard one) is a bit steep, too.