[pigeon] Adds Dart implementation of ProxyApi

[bparrishMines]

Part of https://github.com/flutter/flutter/issues/134777

Pre-launch Checklist

• [x] I read the Contributor Guide and followed the process outlined there for submitting PRs.
• [x] I read the Tree Hygiene wiki page, which explains my responsibilities.
• [x] I read and followed the relevant style guides and ran the auto-formatter. (Unlike the flutter/flutter repo, the flutter/packages repo does use dart format.)
• [x] I signed the CLA.
• [x] The title of the PR starts with the name of the package surrounded by square brackets, e.g. [shared_preferences]
• [x] I linked to at least one issue that this PR fixes in the description above.
• [x] I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy, or this PR is exempt from version changes.
• [x] I updated CHANGELOG.md to add a description of the change, following repository CHANGELOG style.
• [x] I updated/added relevant documentation (doc comments with ///).
• [x] I added new tests to check the change I am making, or this PR is test-exempt.
• [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel on Discord.

[stuartmorgan-g]

(Mostly small comments; There are some big walls of text so I was skimming in the generator, but it looks like the overall structure here is pretty well factored.)

[stuartmorgan-g]

I've reviewed manual versions of the output in webview_flutter in the past, so if you're happy with the generator aspects of this I don't feel like I need to review again.