If I Switch Phones, Does My eSIM Move With My Number Automatically?

I’m planning to move from an Android phone to an iPhone and currently use an eSIM. I’m not sure whether the eSIM transfer happens as part of the phone setup or whether I need to contact my carrier first.

Does this depend more on the phone models, the carrier, or both? I’d also like to know what to check before wiping the old phone so I don’t lose access to my number mid-transfer.