Bakhmut is encircled. All roads in and out of it are under Russian artillery fire. Over the last three days fighting has largely stopped there. No one seems to know why the operation was halted.
There are unconfirmed claims that Ukraine is preparing a counterattack to free Bakhmut from its encirclement. That attack is supposed to go off as soon as the muddy ground has dried up a bit.
Meanwhile other encirclement has taken place in Avdiivka:
Avdiivka (Ukrainian: Авдіївка, IPA: [ɐu̯ˈd(j)ijiu̯kɐ]; is a city of regional significance in Donetsk Oblast, Ukraine. The city is located in the center of the oblast, just north of the city of Donetsk. The large Avdiivka Coke Plant is located in Avdiivka. The city had a pre-war population of 31,392 (2022 est.); in August 2022, its population was estimated at 2,500.
Avdiivka was within the claimed boundaries of the separatist Donetsk People’s Republic, before Russia declared its annexation of the entire region in September 2022. During the war in Donbas, Avdiivka became a frontline city and saw a battle in 2017. During the 2022 Russian invasion of Ukraine, heavy fighting led to Avdiivka being largely destroyed and most of its population having fled.

Source: LiveUAmap
Two week ago the situation suddenly changed. The Russian airforce started to bomb Avdiivka with heavy glide bombs. At the same time an operations was launched to envelope the city from two directions.

Source: LiveUAmap
In the southwest of Avdiivka the Russian forces moved northward. They are currently trying to capture Siverne. The first progress there was stopped when on March 12 the Ukrainian 36th Marine Brigade was placed in the area.
Armed reconnaissance has also taken place into the southwest area of Avdiivka city which is made up of high rises.
The distance between the Russian positions in the southwest and in the northwest of Avdiivka is 8 kilometer (5 miles). That is sufficiently narrow for Russian artillery to interdict road traffic that goes through the area in between.
The landscape around Avdiivka is mostly featureless. There are a few slag hills that rise about 50 meter above their surrounding flatland. But they can be easily covered by artillery and are thus not really helpful for either side.

Source: Ukraine Topographic Map
If the Ukrainian military had plans to relieve Bakhmut with a counterattack it now has to think of the additional problem that the encirclement of Avdiivka brings. Should it start there? Should it split the forces it had accumulated and planned to use for the counterattack in Bakhmut and start a parallel one in Avdiivka? Should it give up on one or both cities? Those are difficult decisions.
I find it likely that the Russian attacks on Bakhmut were halted after the Avdiivka development succeeded to give the Ukraine military enough time to make an error.
Time is on Russia’s side while the Ukrainian military needs to show action and success to keep its ‘western’ support going.
Via https://www.moonofalabama.org/2023/03/ukraine-sitrep-avdiivka.html#more