[webview_flutter] Implementation of the app facing WebViewCookieManager for v4

[bparrishMines]

Part of flutter/flutter#94051

Pre-launch Checklist

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

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

[stuartmorgan]

LGTM

[auto-submit]

auto label is removed for flutter/plugins, pr: 6344, Failed to merge pr#: 6344 with OperationException(linkException: null, graphqlErrors: [GraphQLError(message: Required status check "ci.yaml validation" is expected., locations: [ErrorLocation(line: 2, column: 3)], path: [mergePullRequest], extensions: null)]).