That would also take out Russia's own satellites. And satellites belonging to their potential allies. So, probably not the best move.
And guess which company is best positioned to re-launch a crazy amount of satellites in a very short time. Russia would have to allocate a lot of resources it does not currently have to keep up with SpaceX.
Same orbit or not doesn't matter, what matters is distance, and things in different low orbits (most satellites) are all pretty close to Earth and hence each other when orbits line up. They definitely can't just move satellites away, as satellites have very limited manoeuvring capabilities, and changing orbit takes a lot.
The EMP of Starfish Prime [1], the detonation of a nuclear bomb at 400km altitude (the altitude of the ISS), knocked out streetlights over 1400km away in Hawaii. That means it could have damaged satellites up to at least 1800km altitude (but this was in 1962), which is almost all of the low Earth orbit altitude range. With enough nukes you could probably wipe out Starlink's satellites, but with the way they're spread out, I think you'd wipe out most other satellites too.
I thought there was very little (negligible, even?) fallout from EMP weapons, as there isn't a lot of heavy elements to get irradiated up high in the sky.