fix(chat): identify CLI stream requests

[sriaradhyula]

Summary

• include client_context.source=cli in every AG-UI stream request
• make the client identity explicit for gateways that augment client context
• prevent request validation failures when a gateway materializes client_context and the backend requires source
• add regression coverage for the serialized request body

Why

Some CAIPE gateways add trusted metadata to client_context before forwarding a request. Older CLI requests omit client_context entirely; a gateway can therefore materialize an object without the source required by Dynamic Agents and trigger HTTP 422. Sending the CLI source explicitly is defensive and remains compatible with servers where client_context is optional.

Validation

• bun run test:unit (223 tests passed)
• bunx vitest run tests/stream.test.ts
• bunx biome check src/chat/stream.ts tests/stream.test.ts
• bunx tsc --noEmit
• bun run lint (passes with pre-existing warnings only)