feat: add durable multi-model chat playground

[kauandotnet]

Summary

• add persistent multi-chat UI with model selection before conversation start
• add durable background runs, stream resume, tools, approvals, and observability navigation
• support OpenAI, Anthropic, and Gemini playground providers
• canonicalize durable message state and prevent transcript divergence across consecutive turns

Verification

• frontend: 68 tests, typecheck, lint, and production build
• backend: 30 tests, typecheck, and production build
• browser: consecutive Claude turns and locked model selector verified

Release note

No Changeset: both application packages are private test/demo workspaces and this PR does not change the published root package API.