I've heard the term from Steven Kotkin.
I think it's pretty clear what the term means. It means that nominally the institutions that are meant to protect civil liberties exist, but some person or group has managed to put their hands on enough levers that they can dictate the workings of those institutions.
Like Russia, for example. They have elections for government, and they have institutions that are meant to ensure that the government doesn't have a monopoly on power. In practice however one person has an absolute hold on power, to the point that people who criticize him tend to fall out of windows a lot. That doesn't happen in the US for example. You can trash Biden all you want, no one's gonna show up at your house to murder you.
2. "Socialism" is an economic not a social philosophy. Note how I said "Socially Progressive/Conservative" not economically.
Outside the US+Canada and increasingly the UK, there is a consensus among both Cultural Progressive and Cultural Conservatives that welfare programs can and should be expanded. It is a major pillar of both Christian and Islamic religious political thought (traditionally, capitalism was viewed as negatively due to ursury being a sin - this was the position of the Catholic Church until the 60s).
This is why the German Welfare state (Staatssozialismus) was started by Otto con Bismarck [1] with support from the Prussian nobility as a way to undercut the labor movement in late 19th century Germany. This same doctrinal evolution is used to this day by Socially Conservative parties like the CDU, Likud, BJP, AKP, Fidesz, and the PiS, as well as by Socially Right leaning autocratic leaders like Xi Jingping and Vladimir Putin.
[0] - https://msuweb.montclair.edu/~lebelp/FZakariaIlliberalDemocr...
[1] - https://en.m.wikipedia.org/wiki/State_Socialism_(Germany)
>There is a lack of consensus among experts about the exact definition of illiberal democracy or whether it even exists
I would stop using left/right as a description in politics. For example ruling party in Hungary is socialist, which means it cannot be right wing party no matter what they claim.
[0] https://en.wikipedia.org/wiki/Illiberal_democracy