I don't think it rejects any of those things. When capital goods are privately owned then by definition the workers do not have autonomy or control. If the workers of a coop own the capital goods I would consider that collective ownership of capital goods. Not quite public ownership (you still have to be in the group to access it) but not private either.

Climate critiques are definitely in the realm of capitalism. Your house and your land you use to live on is personal property. But if you are running a factory or a farm for other reasons than for your own use then that then ceases to be personal property and falls into private property which is capitalism.

I've not seen a better difference between capitalism and socialism than capitalism is private ownership of capital goods while socialism is the collective or public ownership of capital goods. Social democrats are not socialist because they are not addressing the ownership of capital goods. They just share the profits via state provided safety nets and benefits.

This understanding is also inclusive of the different forms that socialism can take. State (🤮), Market, or Gift/Library/Communism. I'm open to other opinions on it if someone has critique or a better definition. This is just the one that's made the most sense to me over the last 7 years of me being a leftist