In contemporary political discourse, the terms 'woke' and 'political correctness'and 'Marxism' are often used in unanimity.They can serve as labels for broader cultural conflicts, particularly in debates over social justice, free speech, and the role of ideology in public life etc etc....
This is what is known as these days as 'Cultural Marxism'.
However the 'nanny state' is probably more polemic to 'Marxism'. Marx was opposed to the 'bourgeois society' who saw themselves as 'the civil society' - the elites, the ruling classes, the public service or whatever you want to call those that like lord it over the proletariat.
So why the new elitist left push the 'nanny state' to it's limits is a bit strange. They're all bought into 'Cultural Marxism' but are completely polemic to Marx's thought process of the 'nanny state'.....
I doubt Marx would have supported cancer warnings on alcohol products or mandatory vaccinations for the masses, so why his cortege of 21st century advocates do to the extreme is a bit of a mystery!
They are a strange lot the modern left.