What do you mean with "check the backend"? You can e.g. do assertions on HTTP-responses coming from the backend - is this what you head in mind?
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.
Yeah, specifically that interfacing with the ui causes some side effects we would expect to happen (web hooks sent, reports generated, etc). I definitely wouldn't want to write all of our tests that way, because that sounds like a nightmare to maintain and run, but was considering a handful for covering a few major features. We do already have a very extensive backend integration test suite (http / rest interactions) that doesn't do anything with UIs, though.
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.
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.