There is a Ukrainian breakthrough north of Lyman. With the Russian defence lines broken I imagine they will still have some momentum if a counter offensive doesn't push them back (and lately few Russian counter offensives seem to have been successful).
In fact, I am convinced that the Russians in this whole area have no lines of defence. There was one that was naturally frozen by the Russian offensive limits, but behind it was always a big gap.
It was for these reasons that the Ukrainian breakthrough of the line around Kharkiv made an important opening leading to the collapse of the whole Russian device. Then the Ukrainians stopped along the river, the Russians didn't stop them, they stopped because that was most certainly their objective, an objective that went faster than they thought. So they have capitalised on their gains, they are re-grouping, preparing themselves, recovering the Russian abandonments, searching the annexed areas around Kharkiv which have also been abandoned. Meanwhile the military leaders are making a new plan. The Ukrainians are doing the right thing, not rushing, consolidating their gains, settling down to redo their tactics.
The Russians on the other side, due to the lack of serious defensive positions, are in a bad position, yesterday's aircraft losses in this area illustrate a vacuum of means that pushes the aircraft to take significant risks, they simply have no other options.
It is also this offensive that precipitated Russia to mobilize and organize referendums, they were aware that the Ukrainians have a boulevard in front of them in this area, that the troops of the Kherson pocket are almost trapped and that elsewhere in the South, it is very likely that by piercing the Russian defensive line, the Ukrainians could open a defensive vacuum allowing it to advance as in Kharkiv. Putin is therefore trying to stop the Ukrainians by playing the famous refrain "it's Russia, don't touch me or I'll make a mess of it", playing on the mass of mobilized people to show that it's getting serious. The Russian objective is an attempt at dissuasion to avoid losing the war, a will to take some territories to explain to the Russians that they have "won" even though it is far from what they really wanted to do at the very beginning.
I think that the Kremlin is convinced that it will impose a brake on the Ukrainians to stop the war, I think that they think that declaring these territories as Russian territories will have an effect, that the hundreds of thousands of conscripts will scare them. If this is the case, that this mobilisation is only a dissuasion mobilisation by which it is not given any concrete military role, it will be neglected, they will be sent to Ukraine to make numbers and we will almost not care how they are equipped, trained, commanded. This is the scenario that Putin would like, the one where these referendums and this mobilisation leads Ukraine to capitulate and concede these territories.
But everything suggests that the Ukrainians are continuing the war, pushing the Kremlin to have to ultimately move the mass of conscripts from a position of almost "extras" that the Ukraine will avoid attacking for fear of attacking "Russian" territory to a mass of conscripts who find themselves under fire but are not at all ready. All of this could lead to a large number of human casualties, this mass of people who find themselves in these regions will be seen, there will be large groups, they will have to be housed, transported, etc. The Americans will do what they have been doing since the beginning, transmitting images and coordinates, and the Ukrainians will advertise the HIMARS again. In my opinion, this is another big Russian mistake, where this mass of conscripts will be neglected and thrown into a territory that they think will be safe after their referendums, that it will not be a new Russian army with all its armoured vehicles, artillery and so on that will land on the front, that it will be mostly troops in trucks.