Funny thing about history, words change over time. In the early 1900s when the Italians developed the phrase and coined the word “totalitarian” (in translation, of course), it was viewed broadly as a positive term, just as “dictator” was. At the time, totalitarian meant “Everything within the state, nothing outside the state, nothing against the state.”. It had nothing to do with whether the state was a dictatorial one or a parliamentary one.
Whether you refer to social democracy or the broader concept of socialism, they are totalitarian in the above sense due to their reliance on group identity as well as the specific intent to control and/or manage all of society. By definition and etymology, socialism is group over individual. Socialism subsumes the individual — the individual is to find their identity through their membership in a group, and the state controls what that group is and can do. In socialism that group is historically class based, and that was one of the distinctions that Mussolini and the Fascists based their version: for them the group was the nationality regardless of class. But it was still a group based identity from which one was to define themselves (and, by extension, others).
Thus, socialism at the level of a State is inherently totalitarian. Indeed the recognition of this was one of the key distinction between the Fascists and National Socialists and the “international socialists”. The “international socialists” were seeking a global revolution to socialism via Marx’s failed prediction of the working class rebellion. The Facists and National Socialists saw this as a doomed hope and focused it down to a national level. Their departure was further that they could build national socialist states, and that these states would then conquer non-socialist states until the world was socialist. Thus the difference was between globally totalitarian and nationally totalitarian.
State socialism requires the society to be totalitarian because it is in opposition to individualism. Sure, they proclaimed individualism, but only by virtue of being within the bounds of the state virtues: your individuality is defined by your allegiance and identification with the state. That is a rather Orwellian take on individualism, but that is the socialist state position. Even mechanistically, this is unavoidable.
Mechanically, socialism requires the abolition of private property. Absent private property you have to have group, or state, rule of interactions. To excercise individual control is to counter the socialist construction. As such socialist states must increase the extent in which they control the interactions of their citizens. The individual might not want to bake a cake for someone else. But if we can find some way to control that, either through social pressure that the wants of the group overrule that of the individual or by laws preventing that individual choice, we increase socialism and advance on the path of totalitarianism. Socialism is concerned with the control of the whole of society.
This is also part of why socialism is fundamentally totalitarian, as it requires the whole of the group to be members of the group rather than individuals. Absent everyone entirely volunteering to give up self-identity and being an individual, that requires state control. From there a case can be advanced that totalitarianism leads to, or requires, authoritarianism in the same mechanical means that socialism requires totalitarianism.
Authoritarianism is often what people today think of totalitarianism as. If one accepts that use of the word, then socialism would directly require authoritarianism. The only distinctions would be in how open about that a given group advancing it is, and how long it takes to produce the obvious authoritarianism that can not be swept under the rug. To put it another way: how slowly the heat is turned up.
But in either case, socialism is fundamentally totalitarian in that it requires control of the whole of society, for people to obtain or define their identity through the means accepted by socialist structure, and for the individual to subsume themselves for others.