As others have said, it's really more about the code you're using than the cPanel side of things. The only *real* way to find out will be to upgrade and test it out.
Yes, this is the obvious answer but I wanted to get a preview of what I may be in for. I wouldn't expect much issue with going 7.3 to 7.4 and WHM makes it easy to switch back if necessary. It's more application specific than Cpanel specific but I figure this is one of the forums where you can find a variety of users running a variety of PHP apps that can give insight on their experience.
8.x may be a different story though. It depends on how much that was deprecated in 7.3/7.4 is no longer functional in 8.x. While I understand many of these version upgrades address bugs and security fixes, these may be more important in a large Enterprise-level application environment. With small internal applications (which this is), the saying "if it's not broke, don't try to fix it" comes into play. After 30 years of coding and Sys Admin experience, this saying has served me well and saved countless wasted hours of creating necessarily creating new problems. What is "necessary" can be a matter of opinion and depends on the specific environment. My philosophy has evolved to not letting things get too far outdated, but not being obsessed with being on the latest release of everything.
A whole industry of Sys Admin and consulting services was created by Microsoft over the years due to their finicky, unstable Windows Server. Company's making millions of dollars to keep things running smoothly for companies. Constantly performing updates and fixing issues before and thereafter. It's been so nice to have stuck with LAMP stack the past 15+ years. So much easier to maintain. If a lot of companies got off Windows Server and switched to Cpanel (where the business IT requirements practically allowed), a lot of Sys Admins would be out of a job. LOL. But I'm getting off topic.