It does affect the ability of the Russians to fortify their lines and to resupply their forward troops, if they intend to fire on Ukrainian supply vehicles. They would not be able to bring ammo forward.
And then there will be the effect on Russian artillery. They are dispersed at the moment, but cannot stay that way. They have to displace regularly to avoid counterbattery. There are limited places they can displace to, and limited places where they can be resupplied.
The Russian artillery does not need to disperse to avoid return fire from Bakhmut. Bakhmut lacks shells to return fire.
There will be nothing stopping Russian resupply. Their supply roads are uncontested. Bakhmut is surrounded on three sides and its infrastructure is destroyed. It may be a challenge for the Ukrainians to even execute a withdrawal. If they cannot get out, it will be like Mariupol. They just run out of everything. Muddy conditions may help elsewhere, but will seal the fate of Bakhmut.
The below video gives a good review of the roads in the area of Bakhmut. There are four roads which can be used to reach Kramatorsk and Slovyansk. All four roads go through Bakhmut. If Russia is to reach the two cities, it will go through Bakhmut or off road. Russia controls three of the roads. The fourth road is a smaller dirt road which the Russians are close to.
https://www.youtube.com/watch?v=PqHk9bj4kIA&ab_channel=TLDRNewsEU
Is Bakhmut About to Fall?245,654 views Mar 2, 2023
TLDR Daily:After months of fighting, it seems as if Bakhmut is set for a bloody showdown as thousands of Ukrainian troops could be encircled by Russian forces. So in this video, we break down the recent developments and what this means for the trajectory of the war.