Converts the implementation of the plugin to Kotlin, so that it can be used to dogfood the new async/await support in Pigeon 28 (not added in this PR; this is just to unblock adding that in a later PR).

The process was as described [here](https://github.com/flutter/flutter/issues/188630#issuecomment-4810706280):
- Initial conversion was done using the deterministic Android Studio converter
- I did manual cleanup for some small errors that resulted from the auto-converter, as well as improving nullability in general (e.g., generics in Java can't be annotated, so the auto-converted assumes they are all nullable)
- I fixed warnings and suggestions flagged by Android Studio
- I had Gemini do a local code review focusing on idiomatic Kotlin, and incorporated some of its suggestions to make code more Kotlin-y and less Java-in-Kotlin.

Tests will be converted in a follow-up PR, so that we aren't making massive changes to implementation and tests in the same PR, since it's intended to be behavior-neutral.

Part of https://github.com/flutter/flutter/issues/188630

## Pre-Review Checklist

[^1]: Regular contributors who have demonstrated familiarity with the repository guidelines only need to comment if the PR is not auto-exempted by repo tooling.