I dont think i understand the point about exaggerating (did you mean that?).
You dont have a leftist party like what I'm talking about. One that wants to abolish hierarchies between people. One that guarantees food and shelter for everyone, no matter where they are from.
The socialist party of the entherlands, at least from my short read, wants to stop immigration and identity politics, both are right wing takes.
Your idea of many classes is exactly what actual leftists are trying to get out of your head because it is detrimental to you.
People who receive say unemployment benefits arent another class. They simply dont have a job. Dividing people into classes makes them weak and conquerable.
If you have to sell your time for money, you are working class, like all others. Currently, this working class is under attack by the capital. Incomes for the mahority of people is not going up and by dividing us into many classes we can be told this doesnt concern us.
This leads to folks driving a ferrari through a part of the city where people starve on the streets. That is a sign of fully deleted empathy to your fellow humans.
Actual leftists have the sole goal of destroying homelessness and hunger. Thats what we do.