This is follow up work to #70330.

Since #106607, we now have the ability to add metrics to the log package.

While the original PR adds a metric to track fluentbit connection errors, we should add additional metrics such as:

1. When the output buffer becomes full, the new buffer sink implementation chooses to drop messages instead of blocking the log call (this is a feature). Count these.
2. Count of log messages flowing through the log package.
3. Error counts
4. ???

Use the new infra to add useful new metrics to pkg/util/log, with a focus on improving observability around network logging.

Jira issue: CRDB-11161