Does this itinerary look reasonable?
Yes.
Concerns- the 2nd week of our trip is April 25- May 1. Should we be
concerned about the two Italian holidays?
Are your dates/flights changeable?
You have 13 nights? Can you add nights?
Both holidays fall on weekends so both will be busier than mid week although many will take the whole week off. It will be crowded but it will only get more crowded going in to May. I don’t think changing dates will make much difference- too much earlier you have ferry issues (can be anytime really), weather, later- more crowds.
The tightest most crowded place you are staying is Amalfi. I would try to slot that on weekdays as much as possible.
Both Sorrento and Salerno have more room to move.
If flights can be changed move arrival to 4/17- depart 4/29
It may only be slightly less crowded anywhere. But that eliminates 1 holiday.
4/17 Salerno 4 nights/2 day trips F, S, S, M- visit Paestum, Naples
Weekend passeggiata is delightful in Salerno
4/21 Amalfi 3 nights T, W, TH- visit Ravello, Positano (skip or see from water), hikes, other AC towns
4/24 Sorrento 5 nights/3 day trips F, S, S, M, T - Pompeii, Ercolano, Capri
4/28 Rome 1 night
I don’t think you have much to worry about as far as closures but avoids any travel on either holiday.
Wherever you are for the holiday- enjoy it.
You could do 4-4-4 as well. You have to really fine tune your daily plans before you commit. Try moving dates around if that is possible.
If you can add a night - stay in Rome arrival night and flip the itinerary-
Go to Sorrento first, end in Salerno. Much easier and less expensive to get to Rome from Salerno
Since you'll be staying in 3 locations, plan ahead for how to get you
and your luggage around, transportation in the region is chaotic,
confusing and unreliable. In hindsight we would have spent our arrival
day in Rome after an overnight flight and tried to get some sleep
before having to deal with trains.
This^^
Ferry from Salerno to Amalfi.
Ferry from Amalfi to Sorrento (or driver)
Driver Sorrento to Napoli Centrale, then fast train to Rome
Sometimes you just have to throw money at transportation, especially in this region.