Two things I think.
One the Southern front offensive made great sense because there was a huge propaganda prize at the end, Kherson. Secondly, The Southern front is shorter in length & width with a great natural defensive river, the Dnipro River which had limited bridges and restricted Russian resupply efforts. The Russians realized that they couldn't defend Kherson with the river at their back and no bridges. But Ukraine can defend Kherson with the river as natural defensive line.
The Southern part of the country hasn't been under as much influence as the Eastern part (Donbas). Since 2014 Russian forces have controlled much of this Eastern territory. The East also has a huge natural border with Russia thus making resupply easier. The South is very much more favorable for attack since the front is smaller and the Russians have to bring enforcements either from all the way around and up the single bridge at the Kerch strait or across the narrow Mariupol - Melitopol line which has few East West roads and rail lines linking these areas.
Holding the East has been trading space for time. I wouldn't be surprised if the next Ukranian strike is a strike to retake Mariupol/Melitopol. I think they save taking the Donbas for last.