You need an Azure billing account to connect to your own environment.
Now that they're transitioning their own software to a subscription model, this does sound an awful lot like a cunning wheeze by Microsoft whereby you give them your software and have to rent it back.
Whilst I get the "vision" of software being a sort of cloudy, evolving technosphere where you simply need to deploy a small amount of your own code to orchestrate the existing components in a way that solves your specific problem, I can't see how it's ever going to be practically achievable. It's a security nightmare in the widest sense - you're sharing your hardware, your code and your credit card with a third party (or multiple parties) and don't have any cast-iron assurance that you will ever get anything back, except possibly an extremely large bill. I could understand it if computers were inherently expensive to own and operate and you achieve the same outcome cheaper with a cloud-backed dumb terminal, but any machine capable of supporting this complex hybrid model is within striking distance of supporting the full development environment.
We already have Apple casting developers from the garden on a whim: it's only a matter of time before you need the permission of some large corporation to write any sort of code at all.