In a sense then, anyone on the left in the 21st century is automatically a member of the New Left by virtue of when they are alive.
Would you claim that KKE and the CPRF are "new left"?
The KKE is to the left of Syriza now and AOC ever on border control, wanting refugees and asylum seekers free access to a right to live without being put in concentration camps and a right to sustain themselves in Greece. Makes sense given the KKE is mainly made up of refugees from Turkey.
Admittedly, their policy on same-sex unions and drug reform is at odds with what the New Left believes.
Who says just the New Left supports drug legalization and same-sex unions. A good chunk of the “Old Left” and their political descendants ended up supporting those policies. Just because the gramps doesn’t support it means nothing.
The ossified core of the KKE gerontocratic politburo is lost on the youth league, who on account of being young Grecians support all those things.
The basic problem here is that while 'New Left' refers to a particular political tradition with a fairly clear meaning and definition, 'Old Left' really doesn't except in a sense so broad as to be completely useless. You're basically lumping together all shades of Social Democrat and Communist together as one discrete category and while, yes, they share some ancestry, so do whales and dogs.
You're right, of course, but these days I might actually play the devil's advocate and argue that the commonalities between old-school Social Democrats and Communists are actually underrated, and that they do share a lot in common that distinguishes them from newer currents of leftist thought. There is the common strategic focus on controlling the state apparatus, as I mentioned, and a lot that goes with it such as the organization into parties (with, whenever possible, organic ties with labor). There's the Marxist lineage, as you mention, which even with all the revisions and innovations and reneging, remained clearly present in both. And there is, and I hate to be reductive here but that's honestly the only way I know how to phrase this, a certain seriousness about political power and what it takes to seize it and wield it effectively that is completely lacking among "new left" types.
I dunno man, the Yippies and Situationalists were pretty serious when they were apart of two major protests of which the endgame was gaining political power. The latter of which was crucial in forming solidarity between students and workers.
A lot of this is how you define the “New Left”. If your definition rests on French pessimistic proto-Neolibs and (anti)postmodernists then you may have a point somewhere. If you extend “New Left” to the very mainstream-adjacent like Gore Vidal and Dennis Kucinich then I can see some of it, but then how does the definition not fall apart?