Yes, he calls himself a Democratic Socialist while being a Social Democrat, I’m aware.
Left wing in the modern context refers to anti-Capitalism.
Left-wing has always had a loose, relative meaning, and arguing otherwise isn’t attempting to stop the Overton Window from shifting. It’s just an attempt to gatekeep who gets to be a, “real,” leftist.
No, it’s getting people aligned on terms so proper organizing can happen. Liberals will never align with anticapitalists, for instance.
Right. So, you want to take the term, “left-wing,” which has held different meanings in different contexts over more than two centuries and redefine as exclusively anti-capitalist, so you can tell liberals that they’re not actually left-wing. Now that’s an attempt to shift the Overton Window.