In 2003 Arab parts of Iraq had a population of 20mln and American and British invasion force in March 2003 was 250.000 and Donald Ramsfeld said these forces were not enough.Not sure where these numbers come from.
US had 170K troops in Iraq at its peak fighting an insurgency. Ukraine is only 38% bigger than Iraq size wise.
Also have to remember US fought a Sunni and Shiite insurgency at the same time with a failing nation state. Europeans aren’t like Arabs. Some low grade insurgency might happen here or there, but nothing on the scale we saw in Iraq which required constant troop presence. Nor is there a ethnic war threat like you had in Iraq (Kurds, Shiites, Sunnis).
Once Ukraine falls, MPs will arrive to administer safety to cities and troops and special forces units will chase down any insurgency leaders. Putin will install friendly regime elements that fled the last color revolutions.
But I agree with you that splitting Ukraine in half initially will be the first goal. Wether Putin tries to take the West will probably depend on how the war went and what the West is willing to do to prevent that operation.
Russia sent 100.000 troops to Chechnya in early 2000s against a guerilla force of 50.000 creating a two to one superiority
Ukraine is a country of 45mln people and much larger in size with dispersed population, so 200.000 Russian troops is only enough to occupy half of Ukraine east of Dnepr river.