I've done 2 b2b cruises on Navigator, a 3 day + 4 day in July 2023 and a 4 day + 7 day in May 2024, my experiences were slightly different, even though they were the same ship
July B2B: Got a letter the night before explaining how our room steward would move our luggage if changing rooms and what time to meet in the morning. We met in Star Lounge at 8:30, waited there until 9:30 (Where I assume that was when all other passengers were off) and then we got new keycards which we kept separate from our current keycards. They they scanned us off the ship, we went down to customs...those with passports did facial recognition, those with BC it did take a bit longer. Then we went back to the ship, scanned in with our new keycards, did muster and waited for our rooms to be ready
May B2B was the same as July except after we went through customs, they had us sit in the waiting area of the port terminal for over an hr before letting us back on the ship AFTER the Suites/Pinnacle/Key members.
Not a whole lot of tips to share, but I liked going to the b2b lunch to kill time and then I just hung out at a bar until rooms were ready. One tip I'd give is that if you can stock up on water on the first leg (I'm prime in the casino, so I always have a fridge of water), you can put that in your suitcase and your room steward will move it over and it will not go through any sort of inspections as far as I know so you could have 2-3 cases in there for all they know.