What's the significance of this Russian victory?
What does it allow them to now do / avoid the Ukrainians from doing to them?
The significance is whoever has that slag heap has the eyes over the city. Along with Russian forces moving up from the south west, Avdiivka will be surrounded like Mariupol.
There are 14 000 Ukraine troops in the city that will find it difficult to bring in munitions. The choice will be the Mariupol choice surrender or make a last stand. Of course, the Ukraines can attempt to attack from the north, but the Russian forces will now dig into a defensive position. And wait.
Meanwhile, the forces coming up will move quickly to form the encirclement, even if its the roads that can come under fire. This area is not well fortified, not like Avdiivka and will get artillery pounding, also a lot of troops have moved into Avdiivka.
Then it's a wait and see. Other areas will then become more prominent. The Ukraines are saying there are 400 000 Russian forces in Ukraine, slight exaggeration, and that's not counting those in the Belogrod area. Which concerns the Ukraine's because these may launch an attack on Kharkiv.
In other words, not know where the next attack comes mean reenforcements can only be moved once an attack has begun. Which leaves other areas exposed.
This could be put out to say, we can't go on against such superior forces. So negotiate.