Conduit developer API

### Feature description

When we first started to work on Conduit we prioritized Conduit as a standalone tool. While it's still possible to import Conduit and embed it into your own codebase, we did not put a lot of thought into exposing a nice API for developers. The goal of this issue is to change that.

We should refactor the codebase and hide internals to prevent them from being imported into other modules. At the same time, we want to expose a nice and clear API that allows you to interact with Conduit through code. This will create a clear distinction between the code that's publicly exposed and needs to be backward compatible, and code that's internal and can be freely changed.

This is a prerequisite for https://github.com/ConduitIO/conduit/issues/1268 and https://github.com/ConduitIO/conduit/issues/1274.