Replaces manual method channels with Pigeon.

This replaces all of the method calls in both direction with Pigeon calls, and converts all the top-level objects used for params and returns to Pigeon objects. However, because of the significant object graph, in order to somewhat limit the scope of this PR I made a cut at that layer in the object graph, with nested objects still using the existing JSON serialization. In a follow-up PR, those will be converted to typed Pigeon objects as well, completing the transition.

Unfortunately a significant amount of JSON code can't be removed yet even though it's now unused by the plugin, because it's part of the API of the public wrappers, so clients may be using it. Once all the JSON code is unused, we could `@Deprecated` all of it, and then could do a follow-up breaking change later to remove it.

Most of https://github.com/flutter/flutter/issues/117910