Transportation from Naples to Sorrento

I didn’t even know you could purchase tickets on the EAV website. I would buy it on the spot. There is no need to purchase ahead of time.

Pre-covid we took a ferry from Sorrento to Naples. It was quite painless - from what I remember the boat was like a hydrofoil and it was almost empty. Don't remember the fare but I just checked Rome2Rio and "ferry" is on its list of transfer options Naples to Sorrento.

Well, your experience is par for the course on transportation modes south of Naples. There is no efficient nor fast way to get anywhere. The infrastructure has been sadly neglected. The small roads are constantly congested with traffic.The area is a victim of its Instagram success, but they don't post the honest pic of the realities on the ground. Things just don't work well, crowds are everywhere, even in shoulder seasons, and the response is usually a "oh, well." You need to adjust expectations to appreciate the beauty of the area.
I don't think the Campania Express is really that much better. Once trains start running late, folks just jump on the next one that arrives. No one is checking if it's the Campania or the Circumvesuviana . They all share the single track line. By afternoon, most of the trains are running late, and the journey takes twice as long. When I was there May 2023, by afternoon, no one even tries to check tickets, as folks are standing on the trains in every available space.
We used Aldo Limos. As I remember , it about 100 euros from the Naples train station to your Sorrento hotel. (Even if you use the ferry, you'll,probably need a taxi to your hotel.) Christina in the office is a Brit, and email communication was easy. The drivers were very professional with excellent English. (The trip can be up to two hours one way Naples to Sorrento by car.)
If you can, throw money at this problem, I don't think you'll regret it.
Have a great trip and safe travels.

Unfortunately you aren't at the airport. We took a coach bus from the airport to Sorrento train station for $10.00 The ride was about 1-1/2 hours.

If you feel like a car is the best route (certainly the most convenient), and the timing works, you could soften the blow a bit by adding a little more cost for a lot more impact and have the driver stop at Vesuvio for the Gran Cono hike on the way, or at a winery, or at the villas at Stabiae (the latter being a truly overlooked gem). That’s what I would do esp if you are more than two people. We splurged last time we went using Eurolimos for a few day trips and were really glad we did. It’s just so much easier. And I’m normally a train person.

I would buy it on the spot. There is no need to purchase ahead of
time.

Just echoing Roberto's advice above: just buy tickets when you get to Naples, being mindful that the Express only makes 4 trips a day.

...have the driver stop at Vesuvio for the Gran Cono hike on the way,

This isn't just a stop along the way anymore. You must make timed-entry reservations online in advance, and do that BEFORE you get to the park: their internet service is famously useless most of the time, and they do not sell tickets at the entrance.

I thought the Campania Express was overrated and the Circumvesuviana underrated. Depending on the day and time, either train could be empty or packed. We rode the Campania twice and we were packed tight with little room to move. From Sorrento to Naples we had our carry-on size luggage but it barely fit in the luggage racks above. In fact, my suitcase fell down from above and luckily onto my lap and not onto someone's head.

We rode both several times during our two week stay and ironically, the only day we had to stand was on the Campania from Naples to Sorrento. We finally got a seat about halfway on the 35 minute ride.

I don't know if the logic here is obvious: But I felt we were overcharged by the taxi from the Sorrento Circumvesuviana station to our cliff-front (very close) hotel. That 15-Euro plus tip journey made it easy for me to pay (through the hotel, their land-services partner) 95 Euros (ten years ago) for a car BACK to the Naples rail station.

I agree that in mid-October, you can hope to buy a walk-up Campania Express ticket, as long as you arrive early enough. (I once stood in a long line in the Naples rail station behind Asian customers without a word or English or Italian.) That will also give you a chance to observe the standard Circumvesuviana passenger-loads, and maybe settle for that. You always have the back-up option of a Fixed-Rate Naples taxi to Sorrento. I'd make sure the driver looks at your copy of the flat-rate sheet and agrees to it before you start off. I'd circle the rate. Also, the flat rate sheet states that luggage is included on every Flat Rate trip.

As another reply expresses, correctly, the thought, this is not like Paris, or even like Rome. I don't think 120 Euros, today, is unreasonable for an almost 1 hour drive, and an empty return by the driver. I am not making excuses for southern Italy, but it is not possible to compare the Naples-Sorrento trip to the Rome-Naples trip. It's more like someone flying Business Class to NYC, but then taking the Long Island Railroad to visit friends in Nassau county.