They are liberating Russia

Ukrainian soldiers are leaving Google reviews on local shops as they travel through. I don't think they are looting, but they are definitely stopping for snacks.

you need proper supply chain anyway, the only thing civilians can provide you with is at most food, fuel, and maybe some vehicles. civilians don't have any ammo, radios or any practical communications equipment in general, firearms, mines, grenades, bulk explosives, fuzes, drones, medical supplies, spare parts, and fuckton of other things that you have to supply either way. this is not napoleonic era warfare

Looting happens because people like to steal unusual or valuable stuff. For example, when wristwatches were popular, they were a common item to be looted, because they had a lot of value for their size and weight. It's not about being supplied with necessities.

If you have a proper supply chain and logistics

Do they, though..? Or is it still the classic Russian “wait until the guy in front of you is killed and then pick up his rifle” sort of thing..?

With proper supply chains you can loot more efficiently. Care packages sent back home from the front lines fit nicely on empty supply trucks heading back to restock.

Autocrats can’t keep a strong, smart, well-trained and somewhat autonomous army since they always fear coups.

that's only half of the problem. the other half is that maneuver warfare requires encrypted radios, EW equipment, spotter drones, night vision, good sensors on tanks/APCs/helis, everything has to be mechanized or portable, in other words - lots of expensive kit, and importantly it also requires thorough training to use that kit effectively. russians don't have that. saudis have the kit but no training and their army is crippled by extremely limited agency of field commanders resulting from coup-proofing and petty office politics

russians were able to move freely using deception and surprise against the 2014 ukrainian army. all that training ukrainians have undergone now pays off

I wonder what Ukraine’s long-term game is with Kursk

that's a good question that only maybe 30 people in the world know answer to. kursk oblast has several interesting things, all of which can be used as bargaining chips by ukrainians:

• gas metering station in sudzha. gas is still flowing, but as ukrainians control ground there, their engineers can undo this at ten milisecond notice
• rail lines go from north to belgorod and from there to donetsk. ukrainians now have cut off one of these and if they reach lgov they'll get another one. this is important as russians rely on rail for their logistics backbone https://xcancel.com/Schizointel/status/1823737718582526037#m
• potential of ukrainians capturing kursk npp gets russians paranoid. getting that would be a massive bargaining chip, maybe they'll be able to exchange this for zaporizhian npp
• the captured territory itself would be also useful in negotiations
• ukrainians attacked there because they knew that that part of border is staffed with untrained conscripts. unlike meatgrinder material in donetsk consisting of prisoners and minorities kursk border was staffed with a bit richer, white euro-russians. unlike poor minorities (buryatia republic, for example, had disproportionate number of military deaths, they're also heavily in debt in that region. many tried to get out of debt quickly by signing a contract) these euro-russians have some resources to protest in moscow. ukrainians already captured what could be low thousands of POWs (i've seen number of 2000 few days ago), but all these numbers come from russian telegram channels so take them with a heap of salt. although just yesterday something like 170 were captured, with 130 on video
• then there are psychological and diplomacy effects. ukrainians are the first to occupy territory of nuclear power. incursion like this lifts morale among army, brings war to "i'm not interested in politics" russians at home, and calls bluff on all russian red lines. this already caused germans to pledge more tanks and americans to consider sending JSOW and brits to lift some restrictions on their weapons
• ukrainians maybe decided that that incursion will cause russians to shift some units from east and south to kursk, which would take pressure off of these regions making advance easier, or maybe trigger mobilization which would be a political catastrophe for putin. it looks like hole in kursk is for now just plugged with more of untrained conscripts, but it's unsure if they're ran out of more capable infantry or they don't want to send them there, or maybe logistics haven't caught up by now. at any rate troops in transit are not troops fighting and there were artillery ambushes on entire convoys, in one case destroying 14 trucks and several hundred soldiers (anywhere from 200 to 490) in a minute (in oktabirskiye, on second or third day). there's been another that night. there are also of course smaller ambushes that nobody hears about, because targets are dead and ukrainians don't say anything
• ukrainians are not done, they run in circles around russian units that have no idea what is going on because of their lack of training and effective ukrainian jamming. russians get defeated in detail with arty and air support from across border in sumy region, and it might be that they'll get encircled in south of glushkovsky district, which would bring even more POWs and accomplish something that russians weren't able to do since day one, that is large scale encirclement

all of this comes with a massive caveat that everything we know comes from russian telegram channels, because ukrainians maintain very tight opsec and let out only very little specifically cleared information

this is not what i'm talking about. these cases of wholesale destruction and ethnic cleansing happened after russians controlled territory, not as a prerequisite to advance. it's also quite possible that these units were explicitly ordered to do that, and it's not a result of poor discipline or anything like this