Logs need to go somewhere to be collected, viewed, etc. You might outsource that, but if you don't it's a service of it's own (probably actually a collection of microservices, ingestion, a web server to view them, etc)
In my experience this is best done as an out of band flow in the background eg one of the zillion services that collect and aggregate logs.
In my experience this is best done as an out of band flow in the background eg one of the zillion services that collect and aggregate logs.