setup-python action fails as it cannot find the tool cache on ubuntu-22.04 image

[Codeglitches]

While using the ubuntu-22.04 image on a forgejo runner I was unable to use the setup-python action as it could not find the tools cache (actually it reports it cannot find the right python version in the cache, but is not finding the cache in the first place that is the problem).

Reading setup-pythons documentation on hosted tool cache it states it looks for the tool cache in RUNNER_TOOL_CACHE. However the ubuntu-22.04 image does not have an environment variable RUNNER_TOOL_CACHE, but it does have a RUN_TOOL_CACHE.

When I inject a environment variable RUNNER_TOOL_CACHE with the same value as RUN_TOOL_CACHE the setup-python action works as expected. Is the name RUN_TOOL_CACHE wrong and should it be RUNNER_TOOL_CACHE instead?