Context

Follow-up from PR review on #2638 (review).

Problem

The prometheus loggers and config are currently placed in lmcache/v1/distributed/, but the code that uses them spans multiple modules:

• Integration code is in lmcache/integration
• MP cache engine is in lmcache/v1/multiprocess
• Config is in lmcache/v1/distributed/config.py

The current placement under distributed/ doesn't reflect the broader scope of observability.

Proposed Changes

Move the observability loggers and config to a location that makes sense given the cross-module usage (e.g., a top-level lmcache/v1/observability/ or similar).

References

• [feat] add observability stack to MP mode #2638 (comment)