Social Democracy is socialism insofar as it takes power over investment out of the hands of the capitalist class.
No, they don't really take power out of the hands of the capitalist class, none that I can recall in Europe did it. By allowing that capitalist class to continue to exist, they guarantee that
corruption will within a couple of decades destroy any social-democratic system. And by capitalist class I do not mean the small business of the market economy, the field where competition exists. I mean the big business that supplies the state and is backed by the state.
That is capitalism. The natural monopolies
granted to capitalist rent-seeking, the market-manipulating monopolies enabled and protected by the state's laws (standardization, regulations, "intellectual property, etc). Those will always have a natural interest in corrupting politicians. They will inevitably do it, and use it to increase their power and take over the political system, moving it from social-democracy to oligarchy.
A social-democracy that makes sure these economic fields of activity are not capitalist, rent-seeking, privately controlled, can survive. Not saying that it will, any small businessman can aim for monopoly and seek to get the state on their side, the danger of corruption (from below or even from within the state) is ever present. But it can be managed. Whereas a social-democracy that tolerates large rent-seeking business will
surely fail quickly.
The Democratic Party may once have had within it the monopoly busters. Or was it a different party? I don't know, but you may have once been a party of the small independent business. That is long gone, both parties are thoroughly capitalist, protect the rent-seeker capitalists. The logic that making an ever-greater profit is good, which implicitly says that exploiting people to produce that ever-greater profit is to be protected, is very much supported by both parties. The only veneer of "popular equality" in this game is the allegation that anyone can play at being capitalist, stock markets etc. As if the fact that wealth wasn't getting more and more concentrated didn't disprove that.