“Who holds power” is very abstract and is not part of definition of socialism or capitalism.

Power isn’t abstract, and who holds it is definitional to socialism and capitalism, and to feudalism before them.

• https://en.wikipedia.org/wiki/Dictatorship_of_the_proletariat
• https://en.wikipedia.org/wiki/Dictatorship_of_the_bourgeoisie
• https://www.hamptonthink.org/read/bourgeois-democracy-what-do-marxists-mean-by-this-term

if workers held all the power, would there be homeless?

Not for the most part, no. In your imagined “capitalist” China, did you just assume that they have a homelessness crisis, without even checking? Because you’re unintentionally making our case for us.

Would there be any poor at all?

You can’t go from one of the poorest, least developed countries in the world to universal wealth overnight. But they have made unprecedented progress.

• Helping 800 Million People Escape Poverty Was Greatest Such Effort in History, Says [UN] Secretary-General, on Seventieth Anniversary of China’s Founding
• China’s Energy Use Per Person Surpasses Europe’s for First Time
• At 54, China’s average retirement age is too low
• China overtakes U.S. for healthy lifespan: WHO data