IIRC the whole BTG thing that the Russians were going for was more their attempt at becoming a western-style military with high mobility and extensive reliance on professionals. Them going back to Deep Battle and proper divisional structures was them realizing that building a military that's suited well for fast warfare is no compensation for the sheer volume of fire that the more traditional Soviet model can throw at the enemy.
Which is a microcosm of how out of touch with reality the Russian general staff were prior to the invasion of Ukraine, for western high mobility doctrine to work you must first secure air supremacy, not superiority, supremacy, you then have to obliterate both critical infrastructure (power grid, command structure, rail links, etc), and make sure your army has both a strong NCO corps, and the independence to act on their own initiative at a hugely devolved level. Only then can you invade, and when doing so it must be with relative manpower parity. My basis for this is of course the Gulf war, being the last large-scale NATO military action against what could be called a more traditional adversary (note that I'm not referring to them as a peer, despite the propaganda claims of the time about "the 3rd largest army by manpower", and "Air defences as good as those around Moscow", Iraq was by no reasonable measure a peer), as desert storm was split into two phases, the initial air war, lasting a month, and seeing over 100,000 sorties from Coalition air power, and the ground invasion, which was conducted not before key Iraqi targets were annihilated, which guaranteed total ground flexibility by uncontested aerial recon, and on demand CAS whenever particularly stiff resistance was met.
Russia did none of this, and I do not believe the VKS lacked capability to achieve an at least somewhat similar outcome, had the Russian MoD prioritised procuring the UMPK kits for the FAB series prior to the invasion (notably it was offered at an arms expo in the early 2000s), as well as the now infamous Shahed-136, and their large stockpiles of cruise and ballistic missiles. Russia did launch a series of missile strikes against key Ukrainian air bases during the opening days of the invasion, and made plenty of aerial incursions with combat air patrols (the poor L-39 trainer didn't deserve it though), but this simply wasn't enough to destroy Ukraine's air defences, nor truly suppress their air force. Had they lead the missile campaigns alongside a huge amount of guided bomb strikes during the early days of the invasion, I think the war would have gone vastly differently, but they simply didn't have the foresight, nor did they truly believe Ukraine would resist (leading to many wasted BTGs, and equipment, only to have their alleged ceasefire negotiations scrapped if Putin is to be believed), and now we're stuck with trench warfare, and a VKS which has only recently realised that they can be the decisive weapon in Russia's arsenal.
Sorry for the sperging, I've not really had a place to air my thoughts about Russia's military failings until now really.