1st or 2nd class?

I was traveling on a 1st class pass in January, so here is my experience (your mileage may vary).
Zurich to Bern was very full in 1st class with family groups searching for seats. It is a busy route between Switzerland's political and financial capitals. Lots of business travelers going 1st class.
The rest of the time could be positively lonely in 1st class. It as winter. I took at least one Postbus and there is no 1st class on these, and one mountain railway, the Rigibahn, with no first class. Other mountain lifts, which give you a discount with your STP, also do not have 1st class seats, so you are getting no added value with 1st class.

You could buy a 2nd class STP and purchase upgrade tickets on a selective basis. 2nd class is perfectly comfortable and your luggage should fit in overhead racks.

I think the advantage of 1st class is, as noted, normally less crowded, so more space to
put your luggage, especially if you need the racks at the ends of the car. Overhead
space is usually less of an issue.

Also, given recent comments on the forum about theft, 1st class perhaps less likely
to be targeted? Better chance of keeping your luggage within sight.

does first class offer any advantage for luggage space?

First class usially has more luggage space and it is easier to navigate the wider aisles.

If you are reserving seats and using carry-on sized luggage, then you won't have any difficulty with luggage space in Second class. Only larger bags are a challenge.

Another vote for 1st class. Even Rick Steves travels 1st class on the trains as I learned during a recent episode of Monday Night Travel.

https://www.ricksteves.com/travel-tips/travel-classes/monday-night-travel/summer-trip-report

What's the price difference? That would matter to me. Noting that more than once, we've had non-ICE trains where the second class cars were actually first class, with a "2" placard in the window.

The Man in Seat 61 talks about 1 vs. 2 quite a bit, and there are lots of vlogs where people compare and contrast

The 15-day STP is 723 CHF 1st class and 459 CHF 2nd class. That is a 57.5 % increase, and roughly the difference between the number of seats in equally sized train carriages.

Even Rick Steves travels 1st class on the trains

Business travel for Rick. Tax deductible or he's comped.

I understand that 1st class has wider seats with 3 per row versus 4

The usual seat arrangement on Swiss trains consists of two seats side-by-side, facing another set of two seats, forming a group of four. Occasionally, you may find just two seats facing each other. It is extremely rare to see three or four seats in a row.

For luggage, many trains have a space between one set of four seats and the next, creating a small open triangular area for suitcases (provided they are not oversized). This setup allows you to keep your luggage within sight without occupying seating space - unfortunately it's common to see passengers keeping their luggage with them in a way that blocks others from using the unoccupied seats beside them.

To avoid busy trains, do not travel to or from major cities during rush hour. Use the SBB train app to check the occupancy of each train car (indicated by three little people icons, with three red ones meaning very busy). Sometimes, moving toward one end of the train will bring you to a less crowded area.

As noted by @Sam, you can board the train with your 2nd class ticket/pass and, if necessary, use the SBB app to purchase a 1st class upgrade for that trip or even just a portion of it. You can do this while on the move, before settling into first class.

Personally, I would not spend the money on a first-class pass, but everyone has different priorities, which will be reflected in the various responses to this query.