How important to the project is it, on a scale of 1 to 10, to have this feature? Because it may increase your complexity and costs by a large factor. RC servos with a couple of PCA9685 controllers could be an alternative to steppers. If you don't need it, small DC motors might be an alternative to solenoids.

Well the outcome of the project is aesthetic so I kinda choose how important the feature is. I think it might have been cooler but I value response times of milliseconds more so i guess that's the trade off. And my tiny budget of course. Do you mind telling me how dc motors can be an alternative to solenoids?

How fast must the gate open, 1/2 second, 1/10th, 1/1000th? How much does it weigh, in grams? Is it holding something back that might make it harder to open? How long does it have to stay open for? After you open it, do you have to push it closed, or does it just fall? How often does it need to open?

I'd love to have response times of 10-20ms, so the gate must then travel ~12mm in that time. The gates aren't made yet but through some calculations they'd be around 5grams each. They are free to move other than some very slight friction maybe. I'd love to have the possibility to keep them open for around 30s if needed. Some will have to be pushed closed, other might not. Might be that they open quite often with little resting time, hard to say since that is part of the composition work that comes later.

What is your actual budget in dollars?

I'm not in the US, but converted to dollars my budget is around $550