You just mentioned two tools that their companies are dying, Cucumber and Cypress . With API Testing, you don't have to use them at all.
For dying Cucumber, https://zhiminzhan.medium.com/cucumber-is-dying-what-did-we-learn-725d0f18d95f
For dying Cypress.io, my new article will come out soon. Just check out Gleb's tweet (3 days ago)
https://twitter.com/bahmutov/status/1681271097344380928
I am not saying Cypress API testing worse, simply stated, it makes no sense at all. Use mature httpclient alike library is fine.