EE's traditional contracts have no concept of paying a device off, or of separating your services. You agreed to pay one single monthly fee covering all your airtime & phone, for at least the duration of your minimum term - but ultimately until you explicitly request a change.
Towards the end of your minimum term, the user should receive a text message advising numerous options - which include upgrading to a newer phone or changing to a SIM-only plan. Ultimately though, the choice has to be that of the account holder, thus if no change is requested, none will be made.
Newer plans are often on a FlexPay basis, where you have 2 separate & independent contracts. A fixed-term finance loan for your device repayment, and a rolling minimum-term contract for your airtime. The former naturally ceases when repaid.
It sounds like you would benefit from moving to a SIM-only plan in the short term, and consider a FlexPay plan when you next upgrade.
