At least on genuine apple hardware with a real serial:
The iMessage thing is probably because certain root certificates expired in high sierra and others by now and they can be updated manually. [0]
https://osxchateau.com/articles/updating-ssl-certificates-on...
A bunch expired in 2019 and Apple pushed new installer versions for several OS releases going back to Yosemite. High Sierra made the cut but you don’t have to reinstall [1]
https://tidbits.com/2019/10/28/redownload-archived-macos-ins...
You’d see this if you booted off the CD or recovery partition. an Internet restore should be okay.
You can also get a newer macOS on that laptop altogether using something called OpenCore. I think I stopped somewhere around Monterey but my 2013 clunker would run Tahoe if you wanted it to. I had a newer m1 I just gave away but I had updated the Intel because it was still in mint condition and ran perfectly. I still preferred it to the new one. I just needed a functional browser. /rant