This is exactly the kind of workflow that Bors (https://github.com/bors-ng/bors-ng) automates.
In addition to Bors, there are a number of apps and services that automate this kind of workflow. Here is an incomplete list: https://forum.bors.tech/t/other-apps-that-implement-the-nrsr...
Edited to add: Graydon Hoare (creator of Rust) called this the Not Rocket Science Rule Of Software Engineering (NRSROSE): "automatically maintain a repository of code that always passes all the tests" - https://graydon2.dreamwidth.org/1597.html
Disclaimer: I have contributed code to Bors.