All the parties that use the term use it as a historic relic, because they all at one point espoused an openly socialist ideal, namely, the control of the means of production by the state. They dropped those ideas for a variety of reasons - intraparty conflict, looking to be more moderate than openly communist parties to the left of them, the utter failure of socialism everywhere, etc. However, they all started there, and that's why they're called socialist. Not because "socialist" now magically means something different.

As for Marxism, in the West it's been replaced by a Gramscian false narrative that sees society as oppressive. You can call their bullshit theories critical race theory, critical gender theory, intersectionality, identity politics or whatever else you want. I think it's ultimately a losing argument because it attacks a broad consensus in society in favor of marginalized groups. That in turn alienates the majority. Unless the marginalized groups are somehow able to use the state's military against the majority, they are doomed to failure.