EPIC: Consider AG-UI as client-to-agent protocol standard

[tomkis]

Is your feature request related to a problem? Please describe.
A2A is currently used for both client-to-agent (UI) and agent-to-agent communication. AG-UI is emerging as a de facto standard specifically for client-to-agent interaction. We should evaluate adopting it.

Describe the solution you'd like
Evaluate a dual-protocol approach:

• AG-UI for client-to-agent (UI consumption) — replacing A2A on the UI path
• A2A for agent-to-agent only — keeping it as the inter-agent protocol

Key questions to resolve:

1. What happens to our current A2A extensions that serve UI purposes (form-request, trajectory, citation, canvas, error, agent-detail, settings)? Do they map to AG-UI primitives or do we need to carry them over?
2. What happens to service extensions (LLM, embedding, MCP, form, platform-api) — these are consumed by agents, not UI. Do they stay on A2A?
3. What happens to auth extensions (OAuth, secrets) — needed by both paths. Duplication?
4. What happens to interaction extensions (approval) — UI-facing but triggered by agents. Which protocol owns this?
5. Does the proxy layer (adk-server) need to speak both protocols or can we translate at the edge?

Describe alternatives you've considered

• Keep A2A for everything and continue extending it with UI-specific extensions
• Replace A2A entirely with AG-UI (loses agent-to-agent standardization)

Additional context
Current extension surface that would be affected:

• UI extensions: form-request, trajectory, citation, canvas, error, agent-detail, settings
• Service extensions: LLM, embedding, MCP, form, platform-api
• Auth extensions: OAuth, secrets
• Interaction extensions: approval