Traveling between Sorrento and Rome

Easiest would be to pay a driver hundreds to drive you there.
More realistically for most is to pay for a driver to Naples train station (100-150 euros), then take the high speed train to Rome, transfer to Rome airport. There is a commuter train from Sorrento to Naples train station also.
Most don't recommend doing this on the day of your flight.

Easiest is to hire a private driver
About 500 euros and you’ll need to be in Rome the night before your flight

Please do a search - this topic comes up a lot
There are dozens of threads addressing this

Thank you for the information. It was very helpful.

This direct bus (nice coach) is the least expensive of all options, and probably the easiest. The later bus would be a good option for your evening trip the night before your flight.

https://shop.flixbus.com/search?departureCity=6187d07a-8421-4536-97da-c3f138fd36f8&arrivalCity=40de90ff-8646-11e6-9066-549f350fcb0c&route=Sorrento-Rome&rideDate=10.07.2023&adult=1&_locale=en_US&features%5Bfeature.darken_page%5D=1&features%5Bfeature.enable_distribusion%5D=1&features%5Bfeature.train_cities_only%5D=0&features%5Bfeature.webc_search_persistent_explore_map%5D=0&atb_pdid=ba1a61bf-3cc2-4b80-8db2-3d0a9c675b6f&_sp=4fcead9d-6e2f-4443-b7c4-5809850c5cc2&_spnuid=89ce2136-cad1-43da-8155-3ec2f4842777

Check with the hotel where you're staying in Sorrento. The hotel that we've stayed at a few times in Sorrento has an arrangement with one of the private transfer services. The hotel staff arranged for a private car and driver for us, door to door between FCO and Sorrento for 350 euros (May 2022).