The socialist sense of “private property” refers specifically to ownership of physical (or at least, nonfinancial) means of production, other than by the workers whose labor is applied to it.

It does not refer to all ownership by individuals of real and personal property, restrictions on other personally-held property are separate concerns from the abolition of private property, and socialists regimes, including those in the Soviet bloc, frequently have retained private home ownership, which is not fundamentally inconsistent with socialist theory.

There was a lot of private property in the socialist countries. I am not sure from where this thought even came to you. What was impossible was owning big private enterprise. But small businesses - like a restaurant or a shoe repair shop were allowed. You were also allowed to own houses, cars, appliances, clothes and almost everything else. Land was a bit weird - you could own, but not too much - basically stuff that was small enough to evade the collectivisation process.