The issue of Bakhmut is logistics. Right underneath the bomb and rifle icons in the middle of Bakhmut are rail lines. Controlling Bakhmut will allow Russia to move men an material north and south in the Donbass much faster. This is particularly important for Russia as their miliatary (as I understand it) moves a lot of material by rail.
I won't argue about who has lost more or how many troops in Bakhmut. There is so much propaganda on both sides it is impossible to know. What is clear is that claims by both side that the other side is using "human wave tactics" as a standard is bullshit. If that were true the other side would simply publish satellite photos filled with dead bodies in the streets over and over. We know this could be done after Bucha.
One last point: Noone can point to a failed Russian winter offensive until someone can point to an official Russian statement that there IS or WAS a Russian offensive. It is complete speculation to say that "Russian attacks X, Y, and Z" constitute the Russian winter offensive. Since X, Y, and Z were not complete wipeouts of Ukrainian forces, we declare the Russian winter offensive a failure. It is circular wish-casting.
We won't know for years, if ever, what Russian and Ukrainian losses really have been, or what Russia really was trying for with Kyiv right after their invasion, and/or which offenses by Ukraine and Russia were really supposed to be major offenses. Right now we just don't know.
I just look at the same UAMap as you have in your post and see Russia slowly grinding Ukraine out of the Donbass. I see Ukraine constantly complaining about not having enough weapons, ammo and sometimes also troops.
I'm as sure as I can be that Russia underestimated how difficult this invasion would be. I'm also as sure as I can be that Russia is winning, and as Obama (IMO) correctly stated in 2016, Russia will always have escalatory dominance in Ukraine compared to the West.
The time to negotiate is now if Ukraine wants to stop bleeding out and have a rump Ukraine to hold on to.
