Support structured contextual logging #13646
Description
We should align with upstream changes for logging in 1.35:
- contextual logging kubernetes/enhancements#3077
- Structured logging kubernetes/enhancements#1602
- client-go should log with the context kubernetes/kubernetes#119813
This would mostly just require wrapping context with named loggers at various points within the codebase. This would assist with long-running challenges around figuring out which component is emitting what log message.