[WebIDE] Implement an integration test that verifies code suggestions and duo chat

MR: Pending

Description

Implement an integration test that exercises the GitLab Duo AI capabilities included in the Web IDE. See the acceptance criteria section for the specific behaviors that should be covered by the test.

Acceptance criteria

• Code suggestions appear when typing changes in a file.
• Get Duo Chat responses after sending a prompt.

Implementation plan

• We probably need to mock the API request to obtain code suggestions or chat responses to ensure the test is reproducible/deterministic.