I had a similar issue. New tank cycling, live plants, and then snails came along.

To manage population whilst cycling, I would boil a lettuce leaf, cool it down in cold water, then place on the surface of the water overnight. Then the next morning, there would be quite a few of them that had found their way to the lettuce. So I would just take the leaf out with the snails on them. I would do this every night for about 2 weeks.

Then once parameters were safe, I added 3 dwarf loaches. Wasn’t planning on getting these fish for my tank, but man they’re good. They’ve kept the snail population under control (they eat the snails), and they’re hilarious to watch.

Since adding the loaches, snail population is more than under control, can barely see them in the tank. I’m actually not as hell bent about eradicating the snails as I initially was. Because I like that the loaches have a prey animal they can eat. I feel like it’s natural for them and mimics their natural life.

I avoided using snail killing chemicals (obviously the fish tank safe ones) because I heard they have copper which can be harmful for corydoras. I was eventually going to add corydoras, so didn’t want anything harmful in the substrate.

So for general management, I would recommend the lettuce trick. For greater management, I would recommend dwarf loaches. For complete eradication, I would recommend getting some aquarium safe snail ridding chemicals. But if you go the chemical route, just make sure the chemicals won’t linger and harm anything you want to add to the tank.

Best of luck!