What Architecture is Best Suited for running scalable browsers

I am trying to build a saas product that servers as a helper for a bigger product.

Ideally, I should be able to allow users connect their accounts using OAuth and then make API calls on their behalf to the parent product.

But the product does not have a public API.

My basic solution is -> To to build an server that runs browsers in docker containers, using each users auth-token from the main app to make API calls on their behalf. There are obviously some serious problems with this but is there a better way of achieving my goal?