@owishon not sure, where You came to as "BT Mobile is now defunct"...
No, for the time being, both BT mobile and EE Mobile, same as BT Broadband and EE broadband coexistent...
Yes, You can voluntarily migrate from BT to EE with Broadband, or Mobile. But you don't need to...
If your contract period is now up, you will continue on a monthly rolling basis with your BT Mobile, till You decide as going to re-contract. At that moment, You will more likely need to transfer to EE.
Transfer from BT mobile to EE Mobile is required, as You will be sent out a new EE SIM with a temporary number, and then after this becomes live, your number will need to be ported from BT to EE (for myself, it was an automatic process).
There, most likely EE will refuse to send it out abroad, and will require UK address, presumably your billing/account address to be used.
Be aware, as with EE, different Roaming policies are in place, than are with BT. For example, EU roaming with BT Mobile is still free, but on EE is paid (daily charge, or add-on, or inclusive perk with some plans).
Most likely, You might be charged a little more for out-of-contract with BT Mobile, but at most cases, it will be still cheaper, than the new EE Mobile.
If you were told as you "MUST TO MIGRATE" it's most likely pressure from an operator, to get "sales points", not true...
