Your old computer has Gramps User Directory remnants from Gramps 4.2, 5.1 and 5.2 versions.
The files at the .gramps folder level are common to all the versions. The most important is the grampsdb. But if you’ve used created books of reports, the books.xml is important. The same with place_formats.xml if you’ve made some custom Place display formats. And the thumb folder has all the Media previews used in the Gramps interface.
The version subfolders can sacrifice the view mode and splitbar .ini files without risk. And the version-specific addon plug-ins have to be re-installed from the current repository for each release. But the custom_filters.xml (the rules, parameters and names of your custom filters) and gramps.ini (stores Preferences configurations that are easy to forget) may have SOME content that you want to manually migrate. Those are something to explore with a text editor rather than just copy over to a new version. That’s because they expand readily but are difficult to slim down.
You can run a “Troubleshooting Gramps paths and environmental variables” Python script on your old installation and on the new machine to get a definitive list of how the file locations differ.