chore(vertexai): fork vertexai sdk away from generative ai sdk.

[cynthiajoan]

Description

Fork Vertex AI sdk from dependent from generative ai sdk.
This PR contains breaking changes and will be merged into the GA preparation branch.

Related Issues

Replace this paragraph with a list of issues related to this PR from the issue database. Indicate, which of these issues are resolved or fixed by this PR. Note that you'll have to prefix the issue numbers with flutter/flutter#.

Checklist

Before you create this PR confirm that it meets all requirements listed below by checking the relevant checkboxes ([x]).
This will ensure a smooth and quick review process. Updating the pubspec.yaml and changelogs is not required.

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• My PR includes unit or integration tests for all changed/updated/fixed behaviors (See Contributor Guide).
• All existing and new tests are passing.
• I updated/added relevant documentation (doc comments with ///).
• The analyzer (melos run analyze) does not report any problems on my PR.
• I read and followed the Flutter Style Guide.
• I signed the CLA.
• I am willing to follow-up on review comments in a timely manner.

Breaking Change

Does your PR require plugin users to manually update their apps to accommodate your change?

• Yes, this is a breaking change.
• No, this is not a breaking change.

[natebosch]

There are tests we should bring over from the other repo.

I think the api client tests can likely be copied over directly. The chat tests too, though some might need to be deduplicated. Response parsing tests might need some fiddling, but with more of the parsing logic moving here we'll want to bring over the tests that match vertex.