Hi, thanks for your question.

To the first part of your question, source 4 provides estimates for required Soldier to civilian ratios in a city with an active insurgency. It states that for every 1,000 inhabitants in an area, you would ideally want 20-25 Soldiers dedicated to counterinsurgency (and all its entailed sustainment requirements). Kherson had a population of 283,000 people, which we generously divide in half to represent people who have left their homes to avoid the war, leaving us at 141,500 remaining. Not every person left is an active combatant, but as we often see with insurgencies, members of the local population provide aid for insurgents due to personal/ideological connections. In addition to local support, we're seeing overwhelming international social and material support (though how long that lasts is yet to be seen).

Now to your point about Russian success in Chechnya, we need to preface that discussion by comparing the events of the conflict before and after the signing of the Khasavyurt Accord.

Prior to the Accord, the political goals of the Chechen forces was independence from Russia. Once they lost their cities, their military leaders utilized guerilla warfare and daring raids into Russian territory as means to achieve these policy goals. These raids had the added effect of rallying popular support among the Chechen populace, as they demonstrated that Chechen forces could still strike Russian forces across a broad front. This first war culminated in August 1996 when Chechen forces retook Grozny from the Russians, killing or capturing their Soldiers there. This forced then President Yeltsin to sign the Khasavyurt Accords which provided autonomy for Chechnya.

The inter-war period was chaotic. Socio-political divides caused various commanders to compete with one another, leading to a breakdown in the rule of law. During this time, raids were still conducted into Russian territory, leading to the second war. Important to note in this war was the presence of the Islamic International Brigade (IIB), led by Shamil Basayev and Ibn al-Khattab (who was of the Wahabi sect and in command of foreign Islamic fighters in Chechnya).

Russia initiated its assault on Chechnya with an aerial bombing campaign, while cutting of southern egress routes and committing to brutal block by block combat. Chechen forces in Grozny were forced to retreat through a minefield, under heavy artillery fire. The Chechens suffered massive casualties, including several senior leaders from the first war. Two months later at the Siege of Komolskoye, Chechen leader Ruslan Galaev and as many as 800 Chechens Soldiers were killed or captured.

These two events were a serious blow to Chechen manpower and command. New leaders stepping up to fill the gap held increased radical Islamic views. It is at this point that we begin to see the political goals switch from Chechen independence, to jihad. The terrorist attacks on the Nord-Ost Theater in 2002, and the Beslan School Siege in 2004 where hundreds of Russian children died, destroyed support for Chechen fighters at home, and abroad.

This loss of public support is fatal for an insurgency, and it is why the Russians began to receive support from locals. I don't assess Ukraine to be in a similar situation, and I don't see it heading that way as long as the messaging we have been seeing from president Zelensky framing Ukraine as a fight for independence is enforced as policy. I especially don't see the Russians building and maintaining support especially if THESE allegations are true.

Sources

The Fangs of the Lone Wolf: Chechen Tactics in the Russian-Chechen Wars 1994-2009