have there been states with purely public ownership of the means of production?

Yes, for instance the USSR

"Private ownership of enterprises and property had essentially remained illegal throughout the Soviet era, with Soviet communism emphasizing national control over all means of production but human labor"

https://en.wikipedia.org/wiki/Privatization_in_Russia

Also communist China - under Mao, not the capitalists masquerading as communists in the CCP

https://www.jstor.org/stable/3024256

Also Communist Cuba

https://time.com/5937706/cuba-private-business/

If you don't have mostly complete public ownership of capital, it isn't really Communism. But anyways, these are your textbook Marxist states, and they all have this defining feature