We've been to Nevis 7 times and stayed at 4S about 5 years ago. It was lovely and there are several casual restaurants a short walk down the beach.
4S offers RT transfers from SKB to the resort for $170. This includes greet service, shuttle to Cristophe Harbor and then 4S private boat to the resort on Nevis. It was white glove service a I remember, including helping you with your luggage all the way up to airport check-in on departure.
There is an adult pool at 4S and they come around spritzing you with cool water and offering you water and snacks. You can snorkel off the beach and we saw some fish and a sea turtle. Snorkel equipment was complimentary.

I recommend renting a car so you can explore the island.
Never stayed on St. Kitts but the Park Hyatt looks really nice.

Indian Summer on Nevis gets fabulous reviews but we have not eaten there. Should be no issue with vegetarian food, most menus have options. Definitely the resort would cater for vegetarian or any other special requirements.

The quarantine is down to 24 hours now on arrival. Tests are $150/pp for each test.

I'm biased and like smaller, quieter islands. Our rule is no islands with cruise ports or casinos.