I've tried contact BA IT developers on LinkedIn, they were told to send me on the "Contact us" page.
I did use the "Contact us" page and BA replied asking me to call a phone number. I called and ended up at the regular BA phone line.
After navigating through the options, my phone call was transfered in India to a guy that was absolutely not listening to what I said/tried and was asking me to do stuff I already did. He couldn't even create a ticket for the Web Team and was reading the FAQ page on ba.com...

So... I created a brand new BAEC account and moved all my flights to this account. I was able to login fine before re-opening the app and getting the exact same error !
Seriously BA, ....

There is no way to contact the Web Team, even developers in BA can't do anything. I've lost hope.