Use previous tests output as input for next test

We are doing our best to test a legacy application that quite miraculously has web support.

Is it possible to chain tests and re-use the output of those tests in successive tests?

For example:

1. Test1 creates User1
2. Test2 creates Project1
3. Test3 creates Task1 inside Project1
4. Test4 assigns User1 to Project1
5. Test5 assigns Task1 to User1
6. Test6 deletes Project1

I realize that in a perfect word we would setup and mock the data for each step and run them independently. This is a battle that has been fought and lost . Any solution that insists on that is doomed.

I must find a solution that meets the requirements.

Cypress looks very good, but will it do what I need? Or anything else?