There's some interesting stuff here. I think we might differ on how big of a problem 'woke-ism' is. I would go as far as saying that the term is so thrown about that it isn't really coherent anymore- if it ever was. 'Safe-spaces' has been a conservative talking point for at least a decade, but we haven't seen the collapse of society, and 'cancelling' rarely amounts to right-wing speakers whining about getting flack from having terrible opinions.
That is not to say that there aren't any problems on the left. Any analysis from the left should privilege class and the material concerns of the working class. That is not to say that all issues can be reduced to class, rather we should recognise that racism and misogyny are how class is experienced.
Very often the left try advancing arguments based around identities rather than class. This leads to a situation where the CEO of Starbucks can appropriate progressive discourse and still pay his workers less than minimum wage.
The problem isn't concepts like 'racism' or 'patriarchy'. It is using these concepts without a broader analysis of class. To banish the infighting you describe we need a party that sees how wealth is produced and distributed as indispensable for social justice.
At the moment we have an establishment that simply does not have any good answers to the problems working people are facing. Rather than pursue the necessary policies of economic redistribution, they are instead falling back to nationalistic and anti-elitist tropes. In the lead up to Brexit this paid off for Johnson: the problem is that he doesn't have anything else to offer. Increasingly, it doesn't seem that Labour does either.