So according to your definitions, Javier Milei is a leftist because he threatens the status quo, and those who oppose him are rightists.
I agree: it doesn't have a hard and fast definition.
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wt:socialism#English
(my bold)
1a. Any of various economic and political theories advocating collective or governmental ownership and administration of the means of production and distribution of goods.
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1a. A system of social and economic equality in which there is no private property.
2b. A system or condition of society in which the means of production are owned and controlled by the state.
2b. (Marxism-Leninism) The intermediate phase of social development between capitalism and communism in Marxist theory in which the state has control of the means of production.
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3c. Any of a group of later political philosophies such democratic socialism and social democracy which do not envisage the need for full state ownership of the means of production nor transition to full communism, and which are typically based on principles of community decision making, social equality and the avoidance of economic and social exclusion, with economic policy giving first preference to community goals over individual ones.
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4d. (chiefly Western, often derogatory, colloquial) Any left-wing ideology, government regulations, or policies promoting a welfare state, nationalisation, etc.
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Your definition seems to apply more to syndicalism.
wt:syndicalism
(socialism) Control of government and industry by labor unions, usually achieved through revolutionary direct action.
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Your definition of socialism is so general as to be a bit vague.
Christ wasn't being a socialist as much as philanthropic.
He told the rich man to give everything he had to the poor and follow him, or his remark of the camel through the eye of the needle was anti-rich.
He also had the parable of the 3 people with their talents.
As for rejecting white supremacism, this might be the case of any POC billionaire—presumably Oprah Winfrey rejects the tenants of white supremacism.
FAIK, the US under Jefferson might have been America at its most socialist. Perhaps most of the people were independent farmers and artisans; slaves didn't but presumably they were a minority. Presumably the Indigenous were socialist too. As for women, they might have had more de facto independence and control over their means than de jure.