Hello,
I am trying the preview of GitHub Actions on GitHub Enterprise Sever and found that tool-cahe was hard linked to the public GitHub:
https://github.com/actions/toolkit/blob/main/packages/tool-cache/src/tool-cache.ts#L557

Using the modified context from #576 or process.env.GITHUB_HOST ?? "https://api.github.com directly would solve the issue.

I've not searched yet for other similar issues in the toolkit. This was where the toolkit died first because it didn't have internet access.