I see two reasons as to why they weren't working on Splatoon 3 :
-They were already working on the spin off, probably started production around the release of Octo Expansion (many key designers worked on it)
-They wanted to wait for the result of the Splatfest that would decide on the theme of Splatoon 3 (either Cyberpunk dystipia or Post Apocalyptic dystopia) before starting the production of it, especially if the theme is used for the whole game and not just on the solo stuff. We're possibly talking about clothing design, world design, maybe a few mechanics, etc.
It's not that crazy to actually believe Nogashi when he says prior to that Splatfest that they didn't start production on Splatoon 3. They were transparent enough to straight up tell us that the result of the Splatfest would influence the world of Splatoon 3. Nogashi said they didn't start production on Splatoon 3 when they announced it would influence Splatoon 3, it's not just some Reggie's PR talk.