Just another bit that I think hasn’t been mentioned. I’ve been using Macs for decades, usually outfitted with top specs. I usually update the OS as the new ones appear. Aside from apps that won’t work with newer OS’s, my experience is that there are some cases when an older Mac can run an OS that’s several versions newer than what it came with, and even run apps which have also been updated over that time, the Mac seems to run sluggishly, as if it simply lacks the muscle to move quickly. I most recently experienced this with the 2011 MBAir I finally retired this year: it could run Catalina, but sluggishly, and Mojave was much peppier, so I went back to that (of course, Catalina’s lack of support for 32-bit apps was a bummer, too). My new MBAir (pre-ARM) does fine with Catalina. From what I read, though, others may not have had that impression.
The expired certificate issue was fixed months ago, so that trick only works with installers that were previously downloaded before that time. Any macOS installer fully downloaded from the Mac App Store today are currently certified.
I had the same experience. Some of the Apple links for older systems only worked if I was using Safari.
There is apparently an option for fixing the older installers that was supplied by Randy Singer. Scroll down until you see it:
Like you, I’m working hard to keep my mid-2012 MBP working because of the software I’ve invested in won’t work on the most current systems.