Ferrara Station

Assuming you are travelling on a school day, The 12:35 Regionale seems to depart too early to be used by students.

If there are no seats on the 13:35 Regionale, you can always wait an hour and take the 14:35 one.

I doubt you'll have to stand, by the way. Even if, not for long: students will either let you seat or they will gradually get off at the intermediate stations closer to Ferrara.

We’re actually leaving on a Saturday. Do Italians go to school on Saturdays?

From what I have observed riding the buses, they go for a half day on Saturday.

They are in school at least 30 hours a week (at least for middle and high school). Whether the 30 weekly hours are divided between 6 days (incl. Sat) or 5 days (Mon-Fri) may depend on the individual schools, but many observe the 6 days schedule, which therefore include Saturdays (everybody I know observed that schedule in my years).

So basically Italians are in school 5 hours a day, Mon-Sat, from 8:15/8:30 to about 1:30 with no lunch break (there is only a 15-20 min recess before 11). Lunch is therefore when you get home at about 2pm. I guess that's where we Italians learned to eat late meals.
Elementary schools I think get off a bit earlier (they must do a min of 24 h/week by government decree), but they wouldn't travel by train. The only students who would travel that far from home from the Ferrara suburbs would be high school kids.

Because of the above, as Dario said, a 12:30 train is probably too early to have high school kids on board. There might be other types of commuters as some workplaces observe a half day schedule on Saturdays, so they get off at about 12:30.

We took train from Ravenna- changed in Ferrara then on to Padova on a Tuesday late morning in late September.
Neither train was anywhere near full.