Splatoon 3 definitely needs the option to leave the waiting screen, so you're not forced to wait until something happens.
They must bring back the Squid Jump game and the others, which were excluded from Splatoon 2. Maybe have an arcade full of those Squid-themed subgames. They were only in the original Splatoon, which was on Wii U. All Splatoon 2 had was a jukebox.
Because Splatoon 3 won't be set in Inkopolis, it may not have any stages from either of the previous installments. Cap'n Cuttlefish may not be in the game. He wasn't in the base version of Splatoon 2, but Cap did make his return in the Octo Expansion. Hopefully, it could still be possible to see the Squid Sisters or Off the Hook in some way.
All Ranked Battle types should be available 24/7, sharing the same stages, with every type having a separate rank meter, so you no longer have to wait for the next Tower Control, Splat Zones, etc. They can even have Splatfest Ranked Battles, so you can increase your rank and your Splatfest points at the same time. That way, Splatfests won't be just nothing but Turf War anymore. 2 vs. 2 vs. 2 vs. 2 matches would also make things interesting, so we get four teams in a match. Definitely big improvements over Splatoon 2. Maybe include shooter minigames as well.
They should release a physical version of Splatoon 2 with the Octo Expansion already there. It can be called "Splatoon 2 + Octo Expansion". It may be too late for that, as it's been almost three years since Octo Expansion went live.