Please follow the steps below and check the boxes with [x] once you did the step.
Please provide information about your system and the version of Clementine used.
Tracks from radio streams are scrobbled to Last.fm.
Tracks from radio streams are not scrobbled to Last.fm. However tracks from local library are scrobbled with no issues.
Login with Last.fm account in preferences
Play any station from Soma FM radio stream
Enable scrobble in play bar
Wait for a couple of tracks to be played.

This is not just a Windows issue. I'm having the same behavior on macos. Clementine picks up the artist and track, but doesn't log it into my listens.

What's more is that I can like the song via Clementine, and that shows up in my loved tracks.

Problem also reproducible on GNU/Linux (using openSUSE Tumbleweed RPMs).
Most helpful comment
This is not just a Windows issue. I'm having the same behavior on macos. Clementine picks up the artist and track, but doesn't log it into my listens.
What's more is that I can like the song via Clementine, and that shows up in my loved tracks.