It is known that you must not reuse k in ECDSA; doing so will leak your private key. That's one of the reasons RFC6979 deterministic signatures were invented.
Now, RFC6979 sec 3.6 specifies a possibility of using additional data k' which would feed entropy to the deterministic scheme.
It suffices that the additional data k' is non-repeating (e.g., a signature counter or a monotonic clock) to ensure "random-looking" signatures are indistinguishable, in a cryptographic way, from plain (EC)DSA signatures.
Is reusing k' as bad as reusing k? E.g. could it lead to private key leak?