Personally I wouldn't represent the providers with their own table in the database. Why do you want to model Stripe and Paypal (or whatever) implementation details in your DB? Isn't your DB for modelling your application?
Yes, you do need a table to record which payment method was used. But doesn't the Stripe-specific logic belong in your StripeBilling class (and any other Stripe classes, like StripeApi)?
Ultimately, your application should care whether a payment was successful -- not whether it came from Stripe or Paypal. Yes, you need to keep track of that too, but it shouldn't intrude into your core business logic.
I like to "translate" vendor-specific information -- such as a Stripe subscription webhook -- into a "normalised" format for consumption by my application. And I like to do this as soon as possible.