Replace old JSON implementation of polyline start/end cap with a
structured Pigeon.

https://github.com/flutter/flutter/issues/154737

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] 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], or this PR is [exempt from
CHANGELOG changes].
- [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
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<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/packages/blob/main/CONTRIBUTING.md
[Tree Hygiene]:
https://github.com/flutter/flutter/blob/master/docs/contributing/Tree-hygiene.md
[relevant style guides]:
https://github.com/flutter/packages/blob/main/CONTRIBUTING.md#style
[CLA]: https://cla.developers.google.com/
[Discord]:
https://github.com/flutter/flutter/blob/master/docs/contributing/Chat.md
[linked to at least one issue that this PR fixes]:
https://github.com/flutter/flutter/blob/master/docs/contributing/Tree-hygiene.md#overview
[pub versioning philosophy]: https://dart.dev/tools/pub/versioning
[exempt from version changes]:
https://github.com/flutter/flutter/blob/master/docs/ecosystem/contributing/README.md#version
[following repository CHANGELOG style]:
https://github.com/flutter/flutter/blob/master/docs/ecosystem/contributing/README.md#changelog-style
[exempt from CHANGELOG changes]:
https://github.com/flutter/flutter/blob/master/docs/ecosystem/contributing/README.md#changelog
[test-exempt]:
https://github.com/flutter/flutter/blob/master/docs/contributing/Tree-hygiene.md#tests