If the Discourse devs are as sensible as I think they are, they are not such idiots to do browser support by checking user agents. The right way to do it is to do feature detection on the features themselves.
Supermium seems to follow the Chromium project quite closely, whereas Pale Moon seem to have been forked for Firefox much longer ago. Supermium also seems to at least try to stay close to Google Chrome, whereas Pale Moon really want to build something different.
Given that Pale Moon is a much smaller project, and with how complex browsers are nowadays, I think the Pale Moon developers will have a very hard time keeping up with all the development of modern browsers. I suspect that you’ll run into more compatibility issues by sticking to it.
If I may offer some unprompted advice: Windows 7 has not received any updates in over 4 years, and probably contains many security issues that will not be fixed. If your laptop cannot run Windows 10, I would personally go for a lightweight Linux distribution. At least that way you can run modern, commonly used browsers and keep your device secure.