If you want to test the backend on its own, I personally would recommend using a different framework than cypress (or a different framework than the one being used for frontend e2e testing in general). Otherwise you risk that people conflate these two things and start "testing the backend" in e2e-tests for the frontend, which are super slow.
Cypress is a recent addition for us, so this is more a curiousity than anything else. I've done similar fully e2e / functional tests with puppeteer in the past.
I haven't had much time to try anything yet, but cypress's override of promises and async / await makes me think it'll be a pain to try adding non-cypress-specific checks to a cypress test.
You use Cypress to do something on the frontend, which triggers something on the backend and ideally that change is reflected on the frontend, you test that frontend change using Cypress.
For backend testing just directly call the backend API's and then check the database directly.