I am curious to know to what extent linters such as clang-tidy are in day-to-day use in large projects, as a part of a continuous integration process. Is there a way I can search GitHub for projects that run a certain tool, such as clang-tidy, automatically on every commit or pull request?
I suggest you use a custom search on GitHub, for example, try this search query: clang-tidy language:bash.
Most projects probably use shell scripts written in bash to run clang-tidy. Using language:bash you can easily filter them to find an example suitable for your project. You can view all the available search keywords in the documentation.