docs: clarify AG-UI and CopilotKit A2UI guidance

[samjulien]

Description

This PR updates the AG-UI and CopilotKit references across the A2UI docs for consistency and accuracy.

• Normalizes the product spelling from "AG UI" to "AG-UI".
• Clarifies that AG-UI is the transport/protocol and that CopilotKit is its creator and primary consumer, without conflating AG-UI with CopilotKit-only applications.
• Updates the A2UI + AG-UI guide to preserve broad CopilotKit-supported agent framework messaging while noting React/Next.js snippets and additional app surfaces such as Vue, Angular, and React Native/headless clients.
• Fixes stale CopilotKit A2UI links and clarifies a2ui runtime enablement for dynamic-schema vs fixed-schema flows.
• Adds a Quickstart callout for teams bringing an existing agent app through CopilotKit + AG-UI.

No issue fixed.

Validation

• npx --yes prettier@^3.5.0 --config .prettierrc --check $(git diff --name-only origin/main..HEAD)
• DISABLE_MKDOCS_2_WARNING=true python3 -m mkdocs build
• curl -I -L --max-time 15 https://docs.copilotkit.ai/generative-ui/a2ui
• curl -I -L --max-time 15 https://docs.copilotkit.ai/google-adk/generative-ui/a2ui
• curl -I -L --max-time 15 https://ag-ui.com/
• curl -I -L --max-time 15 https://docs.copilotkit.ai/quickstart

Notes:

• ./scripts/fix_format.sh --check could not run in this local environment because yarn/corepack is unavailable, so Prettier was run directly with the repo config on the changed files.
• python3 -m mkdocs build --strict still fails on eight pre-existing spec JSON link warnings unrelated to this PR.
• npx --yes markdown-link-check $(git diff --name-only origin/main..HEAD) reports pre-existing external link issues for http://opal.google and a Hacker News 429; changed CopilotKit and AG-UI links pass.

Pre-launch Checklist

• I signed the CLA.
• I read the Contributors Guide.
• I read the Style Guide.
• I have added updates to the CHANGELOG. (N/A: docs wording only.)
• I updated/added relevant documentation.
• My code changes (if any) have tests. (N/A: no code changes.)
• If my branch is on fork, I have verified that scripts/e2e_test.sh passes. (Not run: docs-only change.)

[gemini-code-assist]

Code Review

This pull request standardizes the spelling of "AG UI" to "AG-UI" across multiple documentation files, updates CopilotKit integration details, and refines various links and guides. The review feedback suggests clarifying how function execution boundaries are determined at runtime in the custom components guide, and correcting an inconsistent AG-UI link in the data flow documentation.

[contextablemark]

One small comment, other than that looks good.

[ditman]

Comment about the new CTA on the quickstart page, I think it shouldn't be there (or it should be moved all the way to the bottom to a "Learn more"-like section /cc @zeroasterisk?

[ditman]

Thanks for the m-dash cleanse!