See changes here: https://bodhi.fedoraproject.org/docs/user/release_notes.html#v4-0-0
I think fedpkg will likely just work with Bodhi 4 - the interfaces to the client haven't changed, just the results from the server have changed.
I've monkeypatched mine and see no error so far.
Commit b78a5ee2 fixes this issue
Metadata Update from @onosek: - Issue set to the milestone: 1.37