Since last posting, I've had the same adventures as you Aurora! All due to contaminated plants coming in.
There's many species of snails. I had a pond snail and a ramshorn snail come in with plants. These are hermaphrodites, meaning they can breed with themselves so you only need one for it to start laying eggs. I let the one pond snail live for a bit and when it got to adult size it laid 10 egg sacks (each containing 10s of eggs) in a couple weeks! The newly hatched snails are extremely small and invisible. I took out all the baby snails and all the egg sacks I could find, and fortunately that seems to have controlled them. Right now, I have two frogs and they are supposed to eat snail eggs so I have allowed one pond snail to live, but I'm keeping a close eye on the tank for egg sacks!!
Other snails come in one sex and need the opposite sex to breed. Mystery and apple snails are two of these types. I had two females and they never produced progeny. Also, they lay their eggs above the water line so they're easier to see, if I ever get a male. Apple snails come in many colors, they're big and fun to watch with their long antennae. 🙂🐌 There's also snail species that will eat other snails!
Pest snails (and blue green algae) coming in with plants is why it's recommended to put all new plants in a bleach solution before adding to a tank, to kill hitchhikers. IME snails eat a little algae but not enough to control it. Brown algae is eaten by snails and otocinchus, but not slimy blue green algae. It's tenacious. A little keeps reappearing on a rock in my tank. My tolerance for blue green algae is none, because it's toxic to aquarium life and it spreads very fast. I used the blackout method to knock back the algae, followed by a big water change. Then I applied hydrogen peroxide to spot treat the remaining bits. https://smartaquariumguide.com/blue-green-algae-cyanobacteria/
Due to pest snails and algae coming in with plants, I mostly only go to one aquarium shop that keeps their tanks super clean. They're also the only place in town that have otocinchus. They know what they're doing! I've never had a pest come in with their products.