You are correct, Russia did make rapid progress from June to July against Lyman (20K), Severodonetsk (100K), and Lysychansk (95K). However, these are small towns/cities and are not comparable to major cities like Kharkiv (1,400K) or Mariupol (450K), So it's an apples to oranges comparison. Rapid success against small targets doesn't mean rapid success against major cities or Donbass.
Similarly, you are correct that Putin has resounding success against Georgia (3M), Chechnya (1.3M), Crimea (2.4M), Syria (17.5M) in the past. However, these are small countries/territories and are not comparable to major state like Ukraine (37M). Success against small targets doesn't mean success against much larger countries, particularly those with significant US/NATO aid and armaments.
Personally, it appears Putin will adopt the prolonged war strategy due to his disrespect of enemy resistance (emboldened by NATO support), not because he planned all along for a prolonged war like 5D chess strategy based on prior victories in Georgia, Chechnya, Crimea, or Syria. A NATO-backed Ukraine is not a peer-competitor, but much stronger than any enemy Russia has faced in those minor states. Putin should change the rules of engagement to do target dual-use civilian infrastructure, massive troop surge, strategic bombing/missile strike, and treat this as a serious war, not some careless operation.