test: wire end-to-end request flow

[Svagtlys]

Description

Wire and verify the full request flow: User message → Context assembly → Inference → MCP tool calls → Response.

Why

Ensures all backend subsystems work together correctly before individual integration tests.

Scope

• Wire end-to-end flow — TODO Integration chore: set up Python/TypeScript project scaffold and Docker dev environment #1
• Verify each stage passes data correctly