I have been to all of those except Dominica, but when we stopped in Puerto Rico we had flown into Miami to start the cruise and so I already had the ESTA.
Cruise ship passengers generally don't need visas for day stop-offs. (For example, a cruise stop in St Petersburg is a popular way to cross Russia off your bucket list without a visa.)
However, the US doesn't make this exception, so you do need an ESTA to enter Puerto Rico even for a day trip. And since you are departing on the ship from there, and re-entering the US when it docks (you're going to fly home, but they don't know that for sure!), you will definitely need an ESTA.
Dominica, Grenada, Barbados, and Tortola are Commonwealth countries, and you don't need a visa for any of them with a UK passport (and again the cruise ship exception will apply).
St Maarten is an overseas territory of the Netherlands, and Pointe à Pitre is officially a full part of France, but neither is in Schengen and so even if ETIAS has started it will not apply there. And again the cruise ship exception will apply.
The cruise line ought to be able to advise definitively, but I'm fairly confident that you only need the ESTA.
When you're in St Maarten, getting the local bus to Maho Beach (to watch the planes coming in) is a great excursion. It costs about $5 and it's perfectly safe (everyone else on the bus is a tourist). From memory, the bus stop is only a couple of metres from the cruise terminal exit.