How to use TestCafe-Cucumber Node.js project in DevOps deployments
I guess there is no production-ready application or service to solve this task.
However, you can use a REST framework to handle network requests and subprocesses to start test sessions. If you like Node.js, you can start with the Express framework and the execa module.
This way you can build a basic service that can start your tests. If you need a more flexible solution, you can take look at gherkin-testcafe that provides access to TestCafe's API. You can use it instead of starting TestCafe as a subprocess since this way you will have more options to manage your test sessions.