Considering they are working on factions and probably a TLOU2 remaster / patch, couldn't it be late gen before their new game even launches?
I'm assuming they don't make uncharted 5 although they still could.
Factions and a remaster / patch being done is likely by a very small group within the team, I don't think it will hold back The Last Of Us Part 3 even remotely, consider The Last Of Us 1 remaster wasn't done by the entire Naughty Dog team.
Consider The Uncharted Collection was done by Bluepoint games as we still got Uncharted 4.
So I think you are correct that they won't make Uncharted 5, Sony San Diego will likely make that. Naughty Dog Uncharted team is likely working on that new IP, Naughty Dog Last Of Us team is likely starting (or has already started) pre-production for The Last Of Us 3.
Stuff like MPs, remasters, ports are rarely if ever done by the entire team as a whole.
So lets say we get something like
The Last Of Us 2 MP (part of the Last Of Us team)
Naughty Dog Space game new IP (from the Uncharted team)
The Last Of Us 3 (From the rest of the Last Of Us team)
The Last Of Us 1 remake in The Last Of Us 2 engine (Bluepoint games)
Uncharted 5. (Sony San Diego)
Its within reason that all that could happen, simply not by 1 team.