How to factory reset an iPhone with broken screen?

Log in to https://icloud.com/find, choose it from the device list, erase it, then remove it from your account.

Put it into recovery mode by pressing volume up, volume down and then keep holding the side button until you see the computer. Not apple, but computer.

then connect the phone to iTunes or Finder on a computer and erase from there.

Wouldn’t that add activation lock, which can’t be undone because of the broken screen?

No, that will remove activation lock, which the phone probably has already. And if it DOES have activation lock you won’t be able to recover it without the authorization code.