However House was (in FNV anyways) was always primarily concerned with Vegas, and didn't necessarily want to destroy the NCR if they left Vegas untaxed and under his control, so imo blowing up Shady Sands in California seems more like an Enclave move than a House one(The enclave want to destroy all other power structures in the wasteland to become hegemon in north America at least, while House seems content with an 'independent Vegas')

Also in the last episode during Barb's flashback young hank circumvents Betty to sit in on the meeting with House's body double where he first presents the mind-control chip and is diligently taking notes, which seems more like the move of an Enclave spy trying to get as much info on what House is up to to pass up to his superiors than of someone already working for House

And the reveal at the end of this episode that the senator lady's(who was implied to either be enclave or a dupe for them) head was running the mainframe seems like another connection between Hank and the government/enclave

That said Hank's vibes are more business than government, I'll guess we'll see next episode or season