That also matches statements from Russian sources that work is underway in the rear for 90 platoon strongholds and a 40 km long anti-tank ditch.
Yes, those mobilized during May have been beginning to enter the battle. There are also some obituaries or MIA notices of men mobilized in early June. The bulk of the mobilized after the approval of the new law has still have to go in, though (training should indeed be longer than it is, but downtime lengthens the period before going into action); that said, according to some interviews, the situation in terms of manpower is already slightly improving. Some brigades that needed to receive a large number of replenishments to regain combat capability have done so. Staffing of the five new mechanized brigades created in late 2023 (150th to 154th) has mostly been completed, and they are entering the battlefield - some more intensively, others less so. Now the mobilized are going to restore the complement of existing brigades and to staff those created during 2024.
Kostenko also recently reported that the mobilization pace is stable, which should indicate that the very positive figures recorded in May/June are at least being maintained.