Revert "Move client types to internal modules."

This reverts commit 9068d9fc8a88c1655affc76753d5cfc6411716fd.
Revert "Provide `MonadCatchIO` instance and add `runAsync`."

This reverts commit 54b1d3b63109300d6b499bb502571ac031c5221b.
Minimise connection usage.