Is your feature request related to a problem? Please describe.

With #10227, users can set use_internal_logger to false to not use the collector's internal logger for output. In this case, the logs are sent to stdout and there is no way to change this.

Describe the solution you'd like

Add configuration option to the Debug exporter to change the output stream from stdout to e.g. stderr or maybe another file.

Describe alternatives you've considered

Leave this not configurable and have users redirect the standard output from the collector on operating system / console level.

Additional context

When use_internal_logger is true (currently the default), the exporter's output is sent to stderr together with all other logs from the collector. This configurable via service::telemetry::logs::output_paths.