Thinking about Avdiivka.
Situation is similar to Bakhmut, getting slowly encircled. Even more slowly. Relatively large settlement, and I think in a key position. If they can take it, Russians could move it between the two chain of settlements, both providing a defensible line, and crack the inner one, attacking from two sides, starting from the south, at New York, and move further slowly as they advance the front between the two lines.
Ofc who knows what they'll do, what they think they should do, or will be able to do.

As for Ukrainian offensive, it's easy to think in large maneuvers, they regained large patches of land in a quick fashion, so it could make us think they can continue like that in the future.
But all three events had different circumstances. First Russians withdraw from the north, so Ukros moved into empty areas, and run into rearguards. The Kherson and the Kharkov offensives were executed in numerically vastly inferior enemy. On top of this at the Kharkov offensive, Russians were disorganized too.
Now the numbers are beefed up, units dig in, fortifications are built everywhere. I suspect Ukrainian offensive could only be conducted similarly, how the Wagner and neighbouring units do it at Bakhmut. In small patches, surrounding and sieging strongpoints.