Hard to say because the footage and reporting is almost exclusively Russian based.
According to Russian sources, almost every single attack involves at least a company, with up to a battalion sized element in each offensive action. In the last two days, there were 4 points of attack from Orikhiv direction. Around Lobkovo, Nesterianka, towards Robotyno, and West of Novopokrovko. In the beginning of the week, there was an attack in the Vremivsky sector, out of Velika Novosilka at 5 different points. Towards Novodarivka, towards Rivnopil, towards Neskuchne, towards Urozhaine, and towards Novodonetsk.
I don't remember which brigades exactly, but so far elements from three different brigades have been identified, possibly more.
If units were reconstituted shortly after retreating and re-grouping, as few as 3-4 battalions were involved, sometimes breaking up into companies to attack in separate directions (unlikely). If units were fully withdrawn, and fresh ones were sent into battle, you could have upwards of 10 or more battalions involved in this first week of fighting.
Despite heavy losses, these formations can be reconstituted, re-equipped with vehicles, and filled up with fresh recruits. So I wouldn't count these damaged formations as necessarily lost or destroyed.
How much irrecoverable damage has Ukraine sustained? Hard to say, but I would edge towards a conservative estimate. As few as 1-2 battalions worth equipment and manpower could be permanently lost, with the rest re-organized and re-introduced into the fight at a later date.
