Bitcoin is not available as a payment method during account sign-up, though it can be used to purchase account credits once you have created your account. You can then use those credits to purchase your Proton paid plan.
Maybe it's just not available on their mobile web app? I see it when I login to Protonmail (I don't use the VPN though):
There are ways to achieve significant privacy using Bitcoin, the protocol itself is pseudonymous, lightning in many ways enhances privacy. But you need to know what you are doing and there are many gotchas.