runTestnet takes a Conf -> H.Integration a callback, as visible here:

This is a bit meh and we can probably improve that: in the case where the user provides a configuration file, we would like not be tied to the hedgehog-extras/hedgehog APIs like Integration and Property. But this is something we would better do in the future, not in this PR, because it's not required for reaching a first release of cardano-testnet IMHO. And also, it will be some work, because our existing "backend", e.g. cardanoTestnet here is in the Integration monad. So it's not an easy change.

Originally posted by @smelc in #6103 (comment)

This issue keeps track of making possible, in the case where the user is calling the cardano-tesnet executable (as made possible by #6103), to not be tied to a testing monad (the likes of H.Integration and Property). This will be quite a change, because this monad actually spreads to a number of places.