chore: fix and improve some logs

[caicancai]

Motivation:

Explain the context, and why you're making that change. To make others understand what is the problem you're trying to solve.

Modification:

Describe the idea and modifications you've done.

Result:

Fixes #<GitHub issue number>.

If there is no issue then describe the changes introduced by this PR.

Summary by CodeRabbit

• Improvements
  • Enhanced log messages for better tracking and debugging, including more context such as nodeId, serverId, and groupId.
  • Added warning logs to alert users about potential initialization failures in the log storage system.