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

So you are defining an ambiguous term in order to better criticise it? That makes sense, but it might not convince people who have different definitions 🤔

Like I for example would consider a Co-Op where the employees own the company / have voting power over how its run to be a part of a capitalist system, hell, I'd even consider someone who makes a living as an artist where they own all their tools to be a part of a capitalist system... although I suppose that could also be considered socialist to some degree because the artist "owns" the means of production?

These definitions are kind of difficult to use...

I guess it depends on the definition of private property and communal ownership. For me private property is synonymous with private ownership, meaning someone, not everyone, owns the means of production. With communal ownership I don't mean communal society, but rather ownership by a group. For example everyone within a company owning the means of production of said company would be communal ownership.

In that sense I disagree with coops not preventing individuals owning private property in the means of production, because that creates the same frictions that capitalism creates. If someone owns a part of the means of production that you need to create the product, then it creates a situation where they can use that ownership as leverage because without that part you cannot create the product. If their means of production are irreplaceable then they can demand more fruits of labor, because they own a key part of productions, which is essentially what capitalism is. If it's communal ownership there's no leverage because it's for everyone to use and nobody can demand more simply because they own a key part of the production.