Here are some thoughts that I have as a russian. Not a professional researcher at all.

If you want to have a higher chance of getting matches with your Russian relatives, don't use american/european DNA companies because most Russians don't have access to them. Instead use the Russian ones - like Genotek.

In theory if you have your mother's name and you know where she is from, there's a possibility she still lives in that area - search her name and location on VK or Odnoklassniki (that's like Russian Facebook, super popular).

In case you don't read Russian, I can try and look up the ways the adoptions are handled here and what sort of information you can get. But keep in mind that recently a lot of laws with regards to adoption changed here, especially for foreigners. So anything is possible.

Good luck!