Optimize response body handling in logging middleware

[coderabbitai]

Currently, the logging middleware uses json.loads(response.body) to parse the response body for logging purposes. This approach is inefficient as it requires reading and parsing the response stream.

Proposed Solution

Use a custom response class to store the original response data, avoiding the need to re-parse the JSON. This can be implemented following the approach discussed in this FastAPI discussion.

References

• PR discussion: Feature/add request logging middleware #154 (comment)
• FastAPI discussion: How to get Response Body from middleware fastapi/fastapi#7761 (comment)