Thanks for your post! We typically don’t recommend using multiple test suites per project anymore, as we found that for many projects, having a single test case repository and organizing your test cases via sections and sub sections works better than separating your test cases into different test suites. This makes it easier to start new test runs, filter your test cases and navigate between your tests. So we wouldn’t recommend using the multiple suite project mode anymore, and this would also help in configuring the custom fields to specific projects only.
That said, you can still create multiple test case templates that can be used for each separate test suite, although you would just need to handle this organizationally to ensure that your team uses the correct template when creating/editing test cases in each suite (as they would have the option to choose from multiple templates). Hope this helps!