Service layer for both UI and API

[justinyoo]

User story:

AS a developer
I WANT to implement a service layer
SO THAT both UI and API use it to call an LLM

Acceptance criteria:

• A service layer MUST be implemented.
• The service layer MUST inject IChatClient instance.
• The service layer MUST be called by both web API and UI components.

Definition of Done:

• All acceptance criteria MUST pass the test.