[Sebastian]

But my understanding is that this bill is still held up in the Senate and has not received a final vote or Presidential signature so it is not law yet.

So the question remains. Where does BATFE get the authority to start enforcing measures that aren't yet law?

Did you read what I said? The mental health prohibitions are already federal law. They are part of the Gun Control Act of 1968. HR2640 doesn't add any new prohibitions on who can and can't have a firearm, it just provides funding for the states to update their records with NICS, in addition to requiring the states and federal agencies to provide an avenue of relief for people who are prohibited from purchasing or possessing a firearm.