If you ring up EE on 150 they can help you in more detail. If it was added to your EE account from EE direct then the mobile number for the watch will be in your MY EE account.
If you bought the watch separately, away from EE, it needs to be a LTE model and not a Bluetooth only model for the cellular features to work.
From memory, there's no mobile number attached to the watch, you have to ring up EE to activate the eSim who will then give you a mobile number for it. They will tell you what they need from the watch or box.
Just checked on my watch 3 as well - hopefully similar for your Active 2. - go in to Settings on the watch - About Watch - scroll down and is a sub item called " Device " - tap on that and it shows the EID number ( at first said unknown but the number popped up after a couple of seconds )