docs: update legacy Vertex AI for Firebase references to Firebase AI Logic

[jesskuras]

Description of what this PR is changing or adding, and why:

Updates remaining legacy references and documentation links for Vertex AI for Firebase across the GenUI and Flutter AI Toolkit docs and the Flutter AI landing page to reflect Firebase AI Logic and Gemini Enterprise, and aligns Gemini branding wording in the Flutter 3.44 blog post.

Issues fixed by this PR (if any):

N/A

PRs or commits this PR depends on (if any):

N/A

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[gemini-code-assist]

Code Review

This pull request updates various documentation files and website pages to replace references to "Vertex AI" with "Firebase AI Logic" or "Gemini Enterprise", along with updating related links and descriptions. The review feedback points out a grammatical inconsistency in the AI Toolkit documentation and suggests using the singular form "the Firebase AI Logic production endpoint" to align with the rest of the sentence.

[flutter-website-bot]

Staged preview of the updated docs.flutter.dev site (updated for commit b470f87):

https://flutter-docs-prod--docs-pr13925-update-vertex-ai-fireb-4da083d1.web.app

[flutter-website-bot]

Staged preview of the updated flutter.dev site (updated for commit b470f87):

https://flutter-dev-230821--www-pr13925-update-vertex-ai-fireb-d1sd46ph.web.app

[sfshaza2]

lgtm!