The "authoritarian" left is just the framework of every revolution that actually won. There is a very special kind of Western detached romantic chauvinist "left" that believes only in failed and failing pure leftism and tragedy and is shocked and outraged at what it means to win, to establish defenses, to keep a nation or nations running.

There is no liberal left. Liberals are the mainstream political and are by definition conservative under global capitalism.

Depends a lot on where you live. In many countries, communism is simply considered "radical/violent" rather than "authoritarian", and one is not considered a leftist of any sort unless they defend a leftist stance on the economy (progressive views on social issues may not be described as leftist everywhere).

The pure (libertarian) socialists' ideological anticipations remain untainted by existing practice. They do not explain how the manifold functions of a revolutionary society would be organized, how external attack and internal sabotage would be thwarted, how bureaucracy would be avoided, scarce resources allocated, policy differences settled, priorities set, and production and distribution conducted. Instead, they offer vague statements about how the workers themselves will directly own and control the means of production and will arrive at their own solutions through creative struggle. No surprise then that the pure socialists support every revolution except for the ones that succeed.

And the authoritarians try to reconcile this issue by saying we liberals are actually on the right. How wonderful!