The "city" of Soledar lies 18 km (11 mi) from Bakhmut, and its population was 10,490 in January 2022.
The Battle of Soledar began in early August, with Russian forces capturing much of the eastern half of Soledar by September, although being stalled afterward.
As of January 11th, control of Soledar is disputed, with some sources claiming that Russia's Wagner Group were in control of the settlement, while others dispute this version.
A 5 month battle, still disputed.
I think the entire Bakhmut-Soledar area can go either side for now; and then change in a day.
Until and unless one side gets 50km between itself and Bakhmut on either side, there is no way to predict the short-term outcome.
Like the battle for Kherson - it was so iffy until one day it was so clear who had won.