Improve support for logger injection

[tillkuhn]

If used as a library, it would be good if we could provide better support to inject the logger from the client.
Switch to zerolog as it has better context integration support?

• https://danielms.site/zet/2023/custom-zerolog-logger/
• https://github.com/rs/zerolog?tab=readme-ov-file#contextcontext-integration