Yes, this is the intended behavior because a web service worker conceptually exists to provide contents of the web page shown to the user via the onfetch hook.
It's problematic though because 99.9% extensions don't use onfetch, actually they don't need any of the special things that service worker offers except one benefit of running in a separate physical thread, but even that is only really helpful in 1% of time when the extension shows a slow UI and listens to frequent chrome events simultaneously. This is just another evidence that choosing the service worker technology was a mistake, but I don't think Chromium team is brave enough to admit it. A better solution would be to simply add the ability to run the MV2 event page in a separate thread by default e.g. via a key in manifest.json (obviously, it would disable getBackgroundPage methods).
You can suggest a feature request in
https://crbug.com to hide the messages for extension service worker.
The inconvenient workaround is to enable showing just the selected context in console options and choose the context in console toolbar:
Another workaround is to prefix the messages with BG: and use it as a filter in console toolbar: