For what it's worth, there's already a Signature terminal near SFO that private jets can fly in and out of, so Google is just saving the 10 extra minutes it takes to get to SFO by lobbying for a Signature terminal at SJC.
Technically speaking, TSA, who are not federal agents, have to be invited onto an aircraft by the Captain.
They're a federal agency, but not of law enforcement (AFAIK).
As I understand it, they can be comprised of actual law enforcement personnel, including federal. But don't necessarily. And even if a VIPR team included federal law enforcement personnel, it's not clear that they're necessarily acting with federal law enforcement authority.
As if the TSA wasn't a confusing-enough bureaucratic monstrosity.
The old rules are simply not something I'd be confident applies. In the trivial case, sure, a gate agent isn't a federal officer. But if a TSA agent were to appear at a private aircraft, that would be out of the ordinary. And once you start talking about out-of-the-ordinary set-ups, it's worth noting that even a random TSA gate rapist may have out-of-the-ordinary legal authority in some situations. To say nothing of what law enforcement officers may be operating under the TSA's purview in said out-of-the-ordinary set-ups.
I know an attorney who flies their own jet, and if the TSA "agents" are doing something "out-of-the-ordinary", that is the time when there is a "badge check".
I think this is a moot point, as what VIPR teams are typically for securing public transportation or public events, neither of which is a private jet. Air Marshals, although actual federal agents, don't typically fly on private jets unless under Space-A (invited) privileges.
As to what VIPR teams do, a small airport is a VIP away from all sorts of federal officers asking all sorts of questions, private planes or not.