JFK is relatively easy to connect through now all DL flights depart from T4. Which cabin are you flying in on your VS flight?
If you are in Upper Class and your connecting Dl flights are both on the same ticket, you will be able to use the Delta Wing at JFK.
Last time I did this (December 2025) connecting took <1hr with GE and flying in Upper. Once you land at JFK, get through immigration and collect bags, there's a dedicated DL bag drop area to your left as you exit into arrivals. You then need to head upstairs to the standard T4 check-in / security / departures area. There's no separate connecting flight security in T4 anymore (or if there is, it's never open).
Once through security, the walk to the DL departure gates at T4 can take 15-20mins so don't hang around. Some of the gates DL use are right at the far end of T4 B departures. The gate I departed from to FLL was basically as far as you could walk to the very end of the B section departure gates.
Regards
James Mitchell