[config] Investigate how goroutines and Shutdown should be handled in config modules

[TylerHelmuth]

Looking at this some more I really don't like that any component that uses configtls has to add this check. I am worried about components not realizing that the configtls.TLSSetting embedded in confighttp.ServerConfig needs a Shutdown call.

I think it is out of scope of this PR, which is only trying to solve a leak added by existing functionality, but I think we should take another look at how config modules should handle goroutines and Shutdown.

Originally posted by @TylerHelmuth in #9220 (comment)