Improve discoverability of native (BYOK) Claude in the agent host

[TylerLeonhardt]

Context

#323037 (Phases 18–19) adds native / BYOK access for the Claude agent host: when claudeUseCopilotProxy: false host config is set, the Claude Agent SDK talks to whatever claude is configured to directly on the user's own credentials instead of routing through the Copilot proxy.

Today this is a hidden, host-level config flag (agent-host-config.json) with no UI affordance and no guidance when auth fails. This issue tracks making the feature discoverable and the proxy-vs-native choice legible to users.

Ideas

• Auto-disable the proxy when the user isn't authenticated to GitHub. If there's no Copilot/GitHub auth, defaulting to (or falling back to) native BYO removes a dead end where proxy mode can never work.
• Surface the native vs. Copilot choice when picking a model for the first time. Make the transport an explicit, one-time choice in the model picker rather than a buried config flag.
• Show "configure Claude BYOK" docs on an auth error. When a native turn fails with an auth error, surface actionable guidance with a link to docs for setting up your own Anthropic credentials.
• Add a VS Code setting that forwards to the host setting. A workbench-level setting (e.g. chat.agentHost.claude.useCopilotProxy) that pushes down to the agent host's claudeUseCopilotProxy root config, so users don't have to hand-edit agent-host-config.json.