[TODO] Replace codecov uploader with a modern version in GHA #2650
Description
Currently, codecov is called from ci.sh but it uses a long-deprecated version of the uploader. Codecov deprecated their “legacy” uploaders after the breach in 2020 and have since migrated to a unified one. They also have an official GitHub Action that makes use of it. Several months ago, they've started actively deleting the uploading capabilities (and removed the PyPI package, for example).
I think, having custom logic in a shell script brings more maintenance burden than having it in the CI definition directly. Let's move towards GHA, especially since it's not really necessary to make uploads from the local runs outside the CI...