4 days in Sorrento

Just be aware that the Amalfi and Capri each will be a long day. For Naples, it depends what you want to see, but you could get to Pompeii right at opening, spend nearly 3 hours there, then head into Naples. That would leave time for a walk, some Pizza, maybe even the Archeological Museum if that interests you. Day 4? Enjoy Sorrento, you will need the rest.

You can very easily spend 4-6 hours in Pompeii and not see everything. Add in lunch, plus time getting to and from, and most of your daytime is gone. You could spend the rest of the time just exploring Sorrento, since that's where you're staying.

Prem, PompeiI is VAST so you can easily spend the lion's share of a day exploring it unless you've only passing interest in the place. We spent 5+ hours, not including the time to get there and back from Sorrento, and were all in by the time we got off the train in the afternoon. We didn't cover it all in that amount of time, either.

http://pompeiisites.org/en/visiting-info/
This will give you some idea of how big the excavation is:
http://pompeiisites.org/wp-content/uploads/mappa-14-luglio-2022-orario-estivo-scaled.jpg

And this:
http://pompeiisites.org/wp-content/uploads/A-Guide-to-the-Pompeii-Excavations-2.pdf

With what little time and energy you might have left, you might just want to explore some of Sorrento itself? I don't see from your itinerary that you've set aside any for that. :O)

On day 4 we were thinking Pompei and wondered what else we should add to that day

If you do Pompeii properly ( thoroughly) the only thing to add to your day will be dinner back in Sorrento , the evening stroll and a gelato.

You are looking at four very long and probably exhausting days in the heat. You didn’t mention if you are arriving and checking in on day one? I won’t say that it can’t be done, but it will take a lot of energy.

Just saying, to add some perspective to my response regarding Pompeii...Yes, you could spend days there, but when someone says "thinking Pompeii?", at the bottom of a 4 day list, they likely are not going to want to spend 8 hours there in the heat. A simple overview of the site can be done in 2-3 hours (following the Rick Steves tour even), and to be honest, most people probably have seen enough at that point...unless they have a specific interest. My view is, even that is better for the casual visitor than them avoiding going all together. And yeah, been there twice, enjoy history, I might spend longer, but everyone is not me.