I think your last statement best captures what we believe about our Cloud customers: they don’t want to run infrastructure (even if it is Cloud infrastructure). And, we also understand your desire for the same. Specifically, we say that you will love Forge because:
Build apps, not infrastructure: Write an app in minutes while the platform takes care of security, compute, and storage.
In contrast, Atlassian Connect is much more “you build it, you run it.” For the cases you mention, you would surely need to run a database. Just to be clear on your original question, I don’t think we have ever recommended or designed a system where customers run their own database. It might be possible but I’m sure it is not desirable.
Forge storage or entity properties (both linked in my reply above) do seem appropriate for the simple case of “configuration settings based on project or user”. I can even imagine using simple key-value store for the concept of “assignee feedback”, even if there are different grades given by different assignees. Given the right key structure, I know the data wouldn’t be constrained to just the current assignee.
Although we believe key-value stores bring many advantages, they are not a perfect replacement for RDBMS. There are patterns of reading data for which RDBMS is optimized that is not appropriate to a key-value store. You haven’t indicated anything that says you need one, but I’m trying to be clear that Forge storage is not an RDBMS. If you can live with the constraints of key-value storage, then I think Forge is a good solution.