There's a book in Russian, German Noskin, First computers (literally board digital computing machines) for space applications (Герман Носкин, Первые БЦВМ космического применения), ISBN 978-5-91918-093-7.

The author himself participated in many early projects (mostly in hardware) and according to him analog hardware was in favor for a long time, he mentions that space rendezvous tasks didn't use digital computers until the late 70's. Due to this policy many digital computers were really proofs of concept although used in other areas of soviet economics. The first computer according to him used on-board was the Argon-11S (Аргон-11С) on the unmanned missions to the Moon closer to Apollo-8 in time. Also Noskin briefly says that the on-board computer Salut-4 was compatible with general-purpose computers ES used in Soviet economics so it was possible to develop software in PL-1 and Fortran.

There are several mentions of Buran program languages on Russian websites. According to Vladimir Parondjanov, an engineer from the program (Russian Post) three languages using Russian as a base were developed: PROL2 (ПРОЛ2) for onboard programs, Dipol (Диполь) for earth tests, and Laks (Лакс) for modelling. All of them were intended for use not only by professional programmers but also engineers from other areas.

When the Buran program was closed they were merged into a new language Drakon (Дракон, Russian word for "Dragon") that is claimed to be be a "graphical" language having 2-dimensional descriptions of the programs and using arbitrary well-known languages for code generation. This language was also intended for use by non-programmers. The language probably does not have and international community and isn't even well-known within Russia although heavily promoted by its author, Vladimir Parondjanov (the Russian Wikipedia article article is very long and was even deleted once for not following Wikipedia rules). Drakon was first used for programming for the Sea Launch missions and has been used in other Russian space programs since.