Elements of 155th and 40th Naval Infantry brigade have been active in Vuledar, supported by other formations (proxy and army), including one motor-rife brigade (IIRC the 38th, I need to check) plus 2 volunteer battalions identified by Russian/Ukrainian sources.
I do not think that this Vuledar offensive is a major effort, it appears to be an opportunistic and half-hearted local attempt to break into the city by taking advantage of the inactivity of the Z-Oblast for a long time. Now the Russians are shooting the place up with artillery and with Ukrainian reserves deployed there it looks to be positional warfare and another fortified zone. I would not be surprised if in the coming weeks, the Russians do not get serious in Vuledar and the city gradually transforms into a rubble heap.
Rybar did a piece on the last week's combat