Eventually, kids figure out how to use a knife, or not crap their pants.
Early education is about social and emotional development.
I opted to stick my kids in a foreign language immersion program instead.
If it's helpful, this is a more recent one: https://srcd.onlinelibrary.wiley.com/doi/10.1111/cdev.13575 which shows that Montessori preschoolers performed comparably to non-Montessori preschoolers in Kindergarten, though "disadvantaged kids" who attended Montessori schools performed better than "disadvantaged kids" who did not. (My interpretation being the correlation to performance is that the parents got their kids into a Montessori preschool despite economic disadvantages--biased because of what I learned in Freakanomics).
And a tangential analysis: https://www.nature.com/articles/s41539-017-0012-7 that concludes that most studies around Montessori are not sufficient to draw any meaningful conclusions, however adapting Montessori methods into traditional classrooms appears to be beneficial.
Regarding your upcoming decision--if I can offer my advice: find a preschool that best meets your families needs, and not worry too much about academics (at their age). If your children enters grade school with the abilities to succeed in the classroom that's great. If not, it's a great opportunity for them to learn early age how to overcome challenges--which will serve them well when they are adults.
If you want a child to be better at school, conditioning them early to choose from a constrained set of tasks with natural progression seems like a good way to make it comfortable for them.
Do you remember how they measured "success" ?
I really think so too. People are falling over themselves about Early Childhood Education (ECE), thinking they need to start their kids' education as soon as possible or they'll fall behind. It's even in the nomenclature, gotta get them started as early as possible.
Our kid is nearing three. My wife takes her to parks, playdates, mommy and me classes where they do arts and crafts, sing songs, read stories, free play, etc and when she's home she just has free play time. Zero screen policy.
Let kids be kids when they're little and enjoy their childhood a little. They'll grow up and suffer along with the rest of us in due time.
But otherwise we're on the same route as you. ATM the kid is heavily into doing jigsaw puzzles on his own (60 pc is about his limit for DIY), and he likes to read to himself now and then.
Free play is learning for a child. Those are the right things to be doing.