Train transfer times in Italy

Most transfers can be quick because there is little distance involved in the transfer. Step off of one train, walk across platform and get on her next time -- 2 mins. Sometimes you walk to the next platform but far less complicated than airline transfers. We have never had any problems with short transfers unless the incoming train is late. And sometimes the on-going train will be held.

The good thing is it appears most trains are Regionale, which are unreserved and cannot sell out. It also means if you miss the train you had hoped to be on, you can take any Regionale to your destination within the next four hours. Looks like lots of choices, so I wouldn’t be too concerned about the short transfer times, unless you have time sensitive plans on arrival in Siena. Also, I remember seeing train connections posted on the electronic boards at the end of some cars relating to the next station. Not sure if all the Regionale had those.
Siena train station is located below the city. There is an amazing set of moving ‘sidewalks’ and escalators to take you to the level of the city if you choose that way to get up to that level.

In short you don't know how regionale trains tickets work. I'd spend some time on this site: https://www.seat61.com/train-travel-in-italy.htm , aka the Bible of European Train travel, to find the answers to the questions you wouldn't make.
Regarding "non Regionale"" trains, connections are always protected. As long as it's trenitalia's fault and you purchased a through ticket on trenitalia.com. Since non regionale trains have only reserved seats, you must get a new seat reservation for free at the counter on a later "non Regionale" train making the same route.

It really depends a lot on what platform your train arrives and what platform the next train departs from. Sometimes it is on the same platform, therefore all you need to do is alight from a train and walk across the platform to the other train. If the trains arrive and depart at different platform, then you need to walk through the underpass to the platform where the train departs from.

This is a photo of Pisa Centrale Station. Pisa Centrale has 13 tracks arriving in 7 platforms. Trains from La Spezia generally arrive in the middle tracks. Trains to Florence (via Empoli) may depart from any track depending on where they come from (Livorno or Viareggio or just originating from Pisa.

This is a photo of Empoli station. Empoli has 5 tracks arriving in 3 platforms. Your arrival train from Pisa (directed to Florence) will almost certainly arrive at track 1. All Siena trains depart from track 3 or 4 and sometime 5.

So you are almost certain that you will need to change platform by using the underpass (certainly in Empoli, but probably in Pisa too).

If the train is on time, 5 minutes may be sufficient, but regional trains may have a few minutes' delay. I would say that 10 minutes' layover is generally sufficient for those stations. 5 minutes is cutting it close but doable if trains are on time. In any case, if you miss it you just have to wait for the next regionale train, so at most you'll wait an hour and your ticket is good on the next regionale too.

you can see the scheduled departure tracks and arrival track (scheduled track but sometimes they change) for any station in the website below. Just enter the station name in the search box.
https://prm.rfi.it/qo_prm/ricerca_avanzata.aspx

Thank you Frank, SJS and Dario. The reference to the Seat61 site is appreciated.
Straying off the topic a little, do any of you have experience or comments about picking up a rental car at Pisa or Siena train stations?

Thank you Roberto, the link to the pictures helps much with the perspective.

In many stations, you arrive on one platform, and then must go to another platform. For this process, you must descend to the subway (the walkway beneath the platforms), walk to the next, and then go up. If you are like my wife and I, you prefer the elevator.

So, we prepare by getting our things together near the door. Others do as well. We get off, go to the elevator, descend, change platforms, take the elevator up, and we are there. This can take up to 5-6 min.

Note that, in one case at least, the train shifted platforms. We were supposed to be on Platform 9, and it was switched to 1. I had to ask a train person by pantomime what platform. He told me the number in Italian. Luckily we had made acquaintance with some Italian ladies who translated for us.

do any of you have experience or comments about picking up a rental
car at Pisa or Siena train stations?

I don't personally, since I've never picked up in those cities.

However all rental agencies in Pisa are at the airport. You will need to take the PisaMover people mover to go from the station to the Pisa airport (I think it costs 5 euro per person and the ride is 5 minutes).

The rental agencies in Siena are not exactly at the station either, actually they aren't even within reasonable walking distance (Avis Budget is closer but still a long walk) so you will need a taxi from the station.

Since you are coming from La Spezia, if you intend to rent a car, then you might as well rent it from the start. La Spezia has all rental car companies (nearly all located at the cruise port). That is what I would do if you plan to have a car to visit the province of Siena.

If you plan to have a car while in Siena, be aware of the severe traffic restrictions in the historical center. Unless you have accommodations with permitted parking arrangements or outside the historical center, you may need to park at the parking lots surrounding the historical center.