Brief a coding agent to integrate a third-party API

Goal: Add a client for the {{api_name}} API at {{client_path}} (for example src/clients/), and use it to {{use_case}}, so that the rest of our code calls one tested module instead of making raw HTTP requests.

Context:
- The endpoints we need, with the official documentation for each (links or pasted sections):
"""
{{api_docs}}
"""
- Authentication method: {{auth_method}}
- Environment variable names for credentials and settings: {{env_vars}}
- Rate limits, from the documentation: {{rate_limits}}
- An existing client or HTTP module in this repository to use as the pattern: {{pattern_file}}
- Test command: {{test_command}}

Constraints:
- Read credentials only from the environment variables above. Never hard-code, log or commit them, and add the names to .env.example with empty values.
- Base every request and response shape on the documentation above, not on memory, because APIs change. If an endpoint we need is not covered, stop and ask for its documentation.
- Set a timeout on every request. Retry with exponential backoff and jitter, at most {{max_retries}} times, only for network errors, 429 and 5xx responses, and only for requests that are safe to repeat; honor a Retry-After header. Do not retry other 4xx responses.
- Turn failures into our own error types carrying the status code and the API's request ID, with no credentials or full request bodies in the message.
- Handle pagination if an endpoint pages its results, and validate the fields we use from each response.
- Use the HTTP library the pattern file uses. Do not add dependencies without asking. Do not touch {{off_limits}}.
- Tests must not call the real API. Mock HTTP at the boundary with the tool the repository already uses, and cover success, 401, 404, 429 with Retry-After, a 500 followed by success, a timeout, a malformed response and a second page of results.
- Write a short usage section in {{docs_file}}: setup, the environment variables, one example call, and the errors callers should handle.

Done when:
- {{test_command}} passes with the new tests, and the linter and type checker pass.
- A search of the diff finds no credential values, and .env.example lists the new variables.

Verify: run the tests, read the output and iterate until they pass. Then report in this format: Files changed, Client functions, Retry rules as built, Commands run with the last 20 lines of their output, and To test by hand against the provider's sandbox, if it has one. Do not send any request to the live API yourself.