I don't fully understand the relationship but Turkey and Russia have a lot of common interests in the region and in the
Middle East. For example, Syria; and the fact that Turkey is a customer of Russian arms manufacturers.
In Syria, Russia and Turkey have different aims but have been careful not to harm each other directly (mostly). In Northern Syria, Russia and Turkey have joint patrols for example.
I wonder therefore whether Russia's relationship with Turkey, and a wish not to inflame community relations inside Russia (large Armenian and Azeri communities) trumps anything Russia might gain by helping Armenia?
I don't know whether there is any domestic pressure in Russia to help Armenia.
Russia and Turkey have mutual interests - suppressing militant islam.
Russia doesn’t want its former Stans becoming new Afghanistans, neither does Turkey which is busily exporting it’s influence and secular brand of Turkish Islam to its Turkic Stan neighbours.
Russia doesn’t have an Islamist problem, Turkey gets its Ottoman trade Empire back, everyone wins.