You said you can't access the settings I suggested in Message 2. If you're not using the stock Android phone app, it might be worth trying it to see if that does the trick. If it's not already on your phone you can download from Google Play if you have Android 7.0 (Nougat) or later.
That was the first thing I tried last year. All are off on my phone but voicemail activates as soon as I am in roaming and turns off again when I am back in UK. This problem is independant of any settings, either on the phone or by using the voicemail codes.
BT Mobile employees tell me it's down to their network partner, which I believe is EE. I was with EE before moving to BT and I have never suffered this nonsense with them or any other mobile operator.
The really annoying thing is that they don't see it as a serious problem, which it is for people who do not want to use voicemail.
I'm surprised that there is no way to turn it off completely.
All of my services will be out of contract in six months so I'll be looking for another supplier for my £60 a month package, which is a shame because BT Fibre is really good now that Openreach has sorted out my line problems, rock solid 70mbps down 20mbps up.
We have spoken with our product team and they have confirmed that when roaming abroad voicemail is activated automatically and that you do not have the capability to deactivate this. This is how the Voicemail platform has been built. I appreciate that my response will come as a disappointment and for that I am truly sorry.