We have one test suite which tests various upgrade scenarios, but we need to invest into a more comprehensive test suite that can test more.

I'd suggest creating a single test suite that verifies happy path for rules and connectors (I don't exactly know what this is but it does not need to test very specific edge cases or anything). Like the above linked test suite, this one should rely on archive data (instead of rule creation in the suite itself). We then need to create archive data for multiple previous minors representing "typical/expected" rules and connector usages. With this data, we can run an array around the test suite to ensure all archive data works properly on the happy path after any migration on master.