I agree in that it is unlikely that they'll want to pursue the development of two original IPs simultaneously. In my opinion, that's not gonna happen -- Intergalactic will have to do as their "new thing" for the next decade.
In regards to the second game, I don't feel that it is The Last Of Us Part III -- which if it is still in development in any capacity after those Neil Druckmann comments, then it might even be the studio's third game, as well as the one in the most embryonic state at the moment given how Intergalactic seems to be Neil's creative priority when it comes to game development.
If ultimately, the goal for Naughty Dog to release a new game every 3 years and the average development time on these games was 6 years, they'd have to work on 2 games at a time.
That doesn't seem like much of a stretch. Even with one of those games being cancelled.
We're currently nearing 5 years since a release of a net new game, but we know Intergalactic has been in development since 2000. We also know that TLOU Online was canceled officially in 2023. If they started another game at least when this was cancelled, we'd still be in the arena of seeing another game come out by 2029. And that is assuming they didn't already have other projects in the works, which we've heard they did.
Going back to the second game, the Shaun Escayg game, I'm inclined to believe that it might be that rumored singleplayer The Last Of Us spin-off with new characters that was discussed a few months back. It would just make sense to have something along those lines in the pipeline, especially as it must have begun conception at a time in which Naughty Dog were witnesses to both the success of the HBO show and the de-escalation of their multiplayer efforts with TLOU Online. Plus, looking at a potential release date, a spin-off game could very well be made to coincide with the arrival of the HBO show's third season while leveraging the asset work that had gone into the 2022 remake and the canned multiplayer game.
If they took the same time to make TLOUP3 as they did with TLOUP2 (six years) and started today, it would release by 2031... But we also know that Season 1 aired in 2023 and was a massive hit. If they started then, we'd be looking at 2029. Which really lines up with why they might have canceled TLOU, to focus on a single player title as quickly as they could.
I don't think their focus will be spin-offs at this point. I think they at most do one more game in this franchise before moving on to something else.
In a perfect world Naughty Dog would essentially have 3 full sized-ish teams. Two working on franchise games and another working on original IP. As I mentioned before, you really want to be in that new game every 3 years area. It means you generally have two game releases a generation plus a cross gen title, or depending on how it falls two cross gen titles book-ended.
If they were smart, they'd be working on TLOU3 (with a multiplayer mode based on the work they already did), Uncharted 5/Uncharted Reboot ala God of War 2018, and Intergalactic.
They need to figure out some way to keep their franchises alive whether that be through expanding as a studio or outsourcing IP to other studios.