He's dead. The cinematography is very deliberate and it makes no sense at all unless he's dead. The final scene is a waltz:
1. You hear the doorbell ring.
2. You see Tony's face look up.
3. You see the next shot from Tony's point of view.
The extended cut to black, after hearing the bell and seeing his face look up for the final time, is Tony's POV: oblivion.
Chase has said the truth of the ending was set up in the episode before that and all the episodes before that as well. The penultimate episode ends with Tony recalling Bobby telling him how you probably don't even hear it when the mob whacks you. That didn't happen to Bobby, he got riddled with bullets by gunmen right in front of him, so it's included here purely to remind the audience. Earlier in the season, Silvio doesn't notice Gerry Torciano get blown away right in front of him until after it was already over and he later emphasizes this to Tony in a separate scene later, to once again emphasize it for the audience.
David Chaze also recently said he got the idea for the final scene when he passed a similar small diner in Jersey, and told himself "Tony should get it in a place like that." He's dead.
The chorus of the Journey song also builds into the guitar solo as the camera tracks the Man in Members Only Jacket entering the bathroom, as if he is the real star of the scene, in an homage to the Godfather. In the previous season (6"A"), AJ tells Tony he wanted to avenge Tony's shooting because Michael Corleone killing Solozzo and McClusky at Luigi's Restaurant is Tony's favorite Godfather scene, to which Tony replies, it's only a movie.
The Members Only Jacket is also a homage to the title of the first episode of Season 6, where Eugene Pontecorvo kills a fat man with the same initials as Tony (T.S.) while he's sitting down eating in a diner at night. Vito calls out Eugene's jacket in the episode and how outdated it is. The man in the final scene gets acknowledged in the credits by his jacket, despite being more like an extra. A lot of people who don't want to believe Tony dies rightfully ask, if he was whacked, then, who ordered it? It's a good question and there's an answer to it but it partly doesn't matter - it's just another nameless man in a Member's Only Jacket.
This video is the OP is weird, the kid seems to agree Tony got killed but that the audience is whacked before they're allowed to see it, in which case, why wouldn't the cut to black just be Tony dying and it fulfills the same purpose?
To me the much more interesting theory is that the subplot about the Arabs who disappear and are later seen to be fundamentalists actually snuck a nuclear to device into the Port of Newark and detonated it, with the cut to black being sudden nuclear annihilation. It explains why Agent Harris is a nervous wreck for the entirety of the last season(s) after being transferred to Counter-Terrorism, especially in the finale.
The other is that Tony references how, because of his shooting, he has to avoid certain foods or else he could end up back in the hospital, so him stuffing his face with onion rings at the end is him unintentionally eating his way into his death that night.