I’m not sure I understand your question.
Atlassian has three different types of solutions for creating apps for Cloud products (Jira, Confluence, etc): OAuth, Connect and Forge.
With OAuth and Connect, you are basically creating a SaaS product that runs on your own infrastructure. Connect offers you additional integration into the Atlassian host product UI by allowing you to run your web app within an iframe inside the host product. For both OAuth and Connect, strict security applies.
With Forge, Atlassian offers an integrated developer experience in which the app runs on Atlassian infrastructure. Atlassian will take care of hosting, availability and has provided data storage solutions. In addition, the Forge platform hosting solution is currently free of charge. Due to the tight integration with the Atlassian infrastructure, less strict security rules apply.
Atlassian is also working very hard to provide a bridge between Connect and Forge, allowing for more options (for instance in terms of data storage and off-site processing) but with more strict security rules.
In terms of the original question, and my answer, the OP requested whether they could use a relational database with Atlassian Connect Spring Boot. Given that Atlassian Connect runs on your own infrastructure, this is indeed possible.
I hope this gives you a clear overview of the options available for developing apps on the Atlassian platform!