If so, were there any noteworthy differences from contemporary American superheroes? (Note: I don't mean Stalkhanov-style "real" workers who did amazing things, but explicitly fictive characters like Superman.)
The basic answer is no. There are a variety of reasons, but the simplest one is that comics were considered immoral and suitable only for children - if that, since emphasis was placed on the need for children's reading being educational. The first comics journal in Russia - Муха (Mukha) - was founded only as late as in 1991, after movements started forming in the late 1980s.
Let's also not forget that American superheroes typically display inherently individual traits - the opposite of the collective praised in Soviet. So if there had been superheroes, they would have needed to be very different from their American counterparts.
There's always Дядя Стёпа (Uncle Styopa), I suppose - a series of poems turned into animation about an amazing police officer helping others out. Very much not what you asked for, but possible the closest you'll get.
You may find the source interesting, and a post on the Comics Forum is very knowledgable and contains examples. Links below.
Source: Zhuk, Sergei I. "Visual Culture, Media and Cultural Consumption in Soviet and Post-Soviet Russia." Russian History 38.4 (2011): 515-527.
Full source text: https://www.academia.edu/13649798/Visual_Culture_Media_and_Cultural_Consumption_in_Soviet_and_Post-Soviet_Russia
Comics Forum link: https://comicsforum.org/2015/12/09/the-history-of-russian-comics-an-interview-with-misha-zaslavskiy-by-maria-evdokimova/