Diag logger has no context while using OT in large system

[Asafb26]

Diag logger has a really crucial part while debugging a host - for tracing issues or even a non-related logic issue. Currently, the logs dumped by the diag logger have no context, we cannot understand if the log arrived from OT or anywhere else. I guess that we need to label it somehow - a by static label [OpenTelemetry] or custom label for the client choice.

[vmarchaud]

For context this was discussed in https://github.com/open-telemetry/opentelemetry-js/issues/2104

[dyladan]

per-package namespaces are great but there might be value in a host prefix too.

[dyladan]

We now have a component logger. If that doesn't solve your use case please open an issue in https://github.com/open-telemetry/opentelemetry-js as the API package is moving there