I don't know if EE force you to take a watch plan (I suspect they do) in which case you would be linked to EE until that period ended or you cancelled it (check costs).
It would be much easier for you to get the watch from O2.
I have no affiliation whatsoever with O2 or any subsidiary companies. Comments posted are entirely of my own opinion.
This is not Customer Service so we are unable to help with account specific issues.Currently using:
Pixel 7a (O2 & Lyca), One Plus 6 (Sfr), iPhone 12 Pro Max (Vodafone)