The issue isn’t the 21st, it’s the 20th, on that day, there are two general nationwide strikes.
The first, called by the CGIL on October 19th, covers a wide range of sectors, explicitly listing air transport, local public transport, taxis, private hire vehicles (NCC), maritime services, ports, road traffic and safety, freight and logistics, for the FS Group (railways), the strike runs from 9:00 PM on the 19th to 8:59 PM on the 20th.
The second strike ,organized by CLAP, the COBAS Confederation, and SIAL-COBAS, is also a general, nationwide action, however, it was announced on November 5th, two days after you posted your question here, while it excludes rail transport and certain local transport companies, it includes everything else, this perfectly illustrates why it’s necessary to double-check these things, when you asked your question, this strike didn’t even exist yet and hadn’t been announced.
Private shuttle services, classified as "NCC" (private hire vehicles), are explicitly included in the strike.
On November 21st, the day of your flight, there is only a rail-sector strike (involving CUB Trasporti and SGB Ferrovie), covering railways and rail freight from 9:00 PM on the 20th to 8:00 PM on the 21st, there is also a local transport strike for the entire day, but it applies only to a specific list of companies noted in the announcement, the aviation sector is not included in this particular strike call.
Regarding the air traffic controller strike you mentioned I cannot find any record of it, it doesn't appear in the Ministry’s official register for those dates, nor does it show up in the Guarantee Commission’s calendar when filtered for the aviation sector, I’m not saying it doesn’t exist, but it is not present in either of the two official registries. If you read about it somewhere, it would be worth tracing it back to the original source.
If such a situation were to arise, here is how it actually works, because the logic of "the strike is at 1:00 PM, so I’m leaving at 10:00 AM" isn't what matters, the regulations set by the Guarantee Commission for air transport establish two "protected time slots", 7:00–10:00 AM and 6:00–9:00 PM, during which all scheduled departing flights must operate, the same regulation separately guarantees 50% of each carrier’s scheduled intercontinental departures, your flight from Rome to the United States is an intercontinental departure, and 10:00 AM sits right on the edge of the protected slot: inside it, every scheduled departure must operate, beyond it, you are in the 50%.
ENAC publishes a list of flights identified as indispensable, and airlines must request inclusion no later than six days before the strike, so the picture firms up in the final week, your airline is the only one who can tell you about your specific flight, no new strike can be called for the 20th after November 10th, since ten days’ notice is required, the cancellations can still come late, though, so the list is closed but not final.
Regarding the bus, I need to know which company you are using, a direct service from Sorrento to Rome is a long-distance route operated by a private company, not local public transport, general strikes affect local transport in various ways, but the only truly reliable source of information is the notice issued by the operator itself, as far as I am aware, these routes are typically operated by companies like Marozzi or FlixBus.
One last very important point, since you are departing at 6:15 AM, you must keep in mind that the railway strike on the 20th actually begins at 9:00 PM the previous day, these strike periods often start the evening before, so when checking your specific transport operator, be sure to look at the 19th as well.
All this information is taken from the official websites of ENAC and the Ministry of Transport.