Weight, density, if you can put a mark in with your nail. Wood feels like wood, stabilized feels more like plastic. Stabilized is heavy.
Judging from the photos and considering Russians, its likely kiln dried non stab.
You'll need to sand it first, maker has undoubtedly sealed/treated it with something. But I wouldnt ''soak'' it in anything. If you soak it there's no way to control dye absorbtion, could wind up with an aesthetic your not a fan of (just like now). Some grains in the wood absorb more than others and can basically turn black with over saturation.
I prefer to do it in layers to quasi control the color I'm going for, wood stain will work but I myself prefer leather dye
Then again I'm a picky bitch, but I have dyed many a birch handle.