Just a quick remark: Downloading several GBytes of the Intel compiler each time you trigger a GitHub action (typically on each push and PR commit) is a terrible waste of resources. You could use for example the setup-oneapi action to download it only once and store it in the cache of your GitHub project. You can a have a look on the ci-workflow of the Fortuno unit testing framework for an example.
And yes, I absolutely agree: It is a pity, that the NAG-compiler does not provide any support for being used in public CI-workflows (as on GitHub/GitLab). It is my favorite compiler for code development, and many Fortran projects would benefit a lot from that. On the other hand, one can set-up web-hooks to run it on the local hardware triggered by GitHub/GitLab events. (At least in theory, I did not test this myself, yet. I am also not 100%-sure, whether that would be compliant with the licensing terms of the NAG compiler…)