CLI: align PI runtime SDK stream contract

[chubes4]

Summary

• Preserve Anthropic proxy auth headers when constructing the PI model.
• Surface assistant messages carried by turn_end, dedupe repeated assistant events, and treat PI stopReason: "error" as an SDK-style failed result.
• Stream tool-use and tool-result SDK messages from PI tool execution events so recorders/evals observe tool work as it happens instead of only at turn_end.

Stack context

This is a draft stacked PR on top of Riad's PI runtime swap in #3246 (unify-ai-runtimes-on-pi). It is not intended to land independently of that PR.

It also builds on the eval-runner diagnostics that just landed in #3273. Those diagnostics made these runtime contract gaps visible in local SDK-vs-PI benchmarks: without these fixes, PI could look faster while failing to surface assistant output, provider errors, or tool execution in the SDK-shaped stream.

Why

Studio's UI, recorder, and eval tooling still consume an SDK-shaped message stream. This patch keeps the unified PI runtime compatible with that contract while preserving the PI branch's runtime direction.

The main compatibility fixes are:

• WP.com Anthropic proxy auth needs the bearer token in model headers.
• turn_end.message may carry assistant output even when no separate message_end event fired.
• stopReason: "error" should produce an SDK-style failed result, not a successful empty run.
• Tool-use and tool-result messages should stream at execution start/end so evals and recorders can observe real tool work.

Testing

• npm test -- apps/cli/ai/tests/pi-runtime.test.ts
• npm -w wp-studio run typecheck
• npm run cli:build --silent
• Local SDK-vs-PI rig benches using the shared homeboy-rigs eval scenarios:
  • studio-agent-runtime
  • studio-agent-site-info

AI assistance

• AI assistance: Yes
• Tool(s): OpenCode (GPT-5.5)
• Used for: drafted the PI runtime contract fixes and regression tests, then ran local validation and benchmark comparisons. Chris directed the benchmarking scope and reviewed the findings.