question regarding whether a shore excursion should be taken or do it on your own

I have not been to all of those ports but I was in Palma de Mallorca last year from a cruise and we did it on our own. We made reservations for the Palace ahead of time.

I suggest that you look on Facebook and Cruise Critic for others going on this cruise to find the information you want.

I have also used Trip Advisor to compare independent excursions to the ship excursions. Deciding between a ship excursion and visiting a port independently is a personal choice.

Enjoy your trip.

I am no help on these specific ports, but I can give some general hints about shore excursions. The further that you plan to be from the port on your excursion or if the excursion is a long one getting back close to all aboard time, then the better it is to take the ship excursion. If you are planning on staying in the immediate port area or nearby, then an alternate excursion company might be a fine option. You can also simply explore the port area on your own. The suggestions to look to some of the cruise centered forums was a good one.

Ship shore excursions are almost always the most expensive. Often you can purchase the same shore excursion in the dock area for about 20% less. What you don't get is the guaranteed return. I think 99.9% of the time this really isn't a big issue as the private operators are well aware of the importance of getting visitors back to the ship prior to sail away. I will say, that on my last cruise, there were late excursion buses in two ports. They were ship excursion buses that had been due back exactly at sail away time and we waited 30 minutes for those passengers each time. I'm pretty sure those passengers were glad they had purchased a ship excursion.

My feeling is that Palma is the short port day, and I believe that the new port is a fair way out of the City Centre.

I suspect that if you tried to replicate Soller (which is what I would be tempted to try to do, personally) and have lunch there you would be a bit pressed for time.

On that basis I suspect I would make Palma my shore ex port to make best use of the limited shore time.

St Tropez is a tender port I believe, Olbia and Messina you are supposed to have centrally located berths I understand

...The further that you plan to be from the port on your excursion...the better it is to take the ship excursion.

Carol now retired is spot on. If you are on a ship excursion and are "late" getting back, the ship will wait for you. Not so if you are on your own. We've done many cruises and have seen people running along the pier as the ship departed. Ship excursions will probably cost a bit more, but not as much as having to get yourself to the next port to catch up with the ship.

I didn't find Messina very exciting (Sicily has a lot of more interesting places), so l'd be hoping to go elsewhere that day. I do no know how practical that is, but I think a cruise excursion would be a safer option..

We have done 21 ocean cruises and do occasionally take the ship's excursion.
There are actually three choices:
1) Ship's excursion
2) Do the port on your own
3) A Private Excursion

First, do your research for the port or areas near the port to determine WHAT you desire to see. TripAdvisor.com is a great source for this, just check "things to do."

Then find private tours, here is one of the sources for finding private tours, https://www.shoreexcursionsgroup.com
Compare the ship's excursion against the private tour. If the price is about the same and coverage about the same, stick with the ship's excursion. Generally, private tours are cheaper and you don't have as many others on the tour bus with you.
Still, some port are amenable to doing it yourself. If the sites you wish to see are within walking distance and convenient, then that might be worth a try, but most of the time you can maximize your experience by taking a tour.

I haven't been to any of these ports, so I can't provide any practical experience.