I don't recall the exact context anymore but during the Microsoft Build this year it was said by an employee at Github that the service came with the acquisition which is the reason it was and stays C#.
You can also find many leftovers with the "VSS" acronym, like https://github.com/actions/runner/blob/main/src/Sdk/Common/C... or https://github.com/actions/runner/blob/main/src/Sdk/Common/C... - which also mentions TFS (which is yet another acronym that used to refer to the Microsoft team-development thing).
This probably answers your question:
https://github.com/actions/runner/blob/a4c57f27477077e57545a...
For anyone who was at Github at the time, was it always written in C# or rewritten/replaced after acquisition? If "GitHub Actions is based on Visual Studio Team Foundation Server's CI" is the case, then it sounds like the latter.
[1]: https://github.blog/2018-10-16-future-of-software/