Definitely the US, but the goal for both the Soviets and US was to prop up some quisling state that immediately fell apart the moment each state departed. The Afghani could never have taken on either state if the goal was Medieval or Ancient tier conquest featuring large scale genocide and enslaving of the people. The "Graveyard of Empires" shit is so trite because its just outright wrong. The Mongols steam rolled the region, the Islamic Calpihate steamrolled them and destroyed all of their local religions, the Persians owned them and Alexander literally founded Kabul, Herat, and Kandahar. The only reason the Afghani managed to dunk on the British, Soviets and Americans is because all three refused to just genocide 50% of the population for ideological reasons like the past invaders.
Sort of. Ancient conquerors did massacre a lot of people, but many were enslaved or surrendered rather than killed outright, so losers of wars didn't take anywhere close to 50% dead most of the time. Genocides happened sometimes; the Mongols exterminated the Khwarezmians in revenge for killing their envoys. But ancient scholars liked to exaggerate the sizes of armies and how many men they killed, so taking that into account it's worth noting that many ancient wars didn't actually have the colossal death tolls some period sources suggest in reality (though deaths from famine and disease certainly left a hefty impact, and Alexander the Great had no qualms about killing rebels).
When considering that, and that millions of Afghans have died in constant low-intensity war since the 1970s, the degree of bloodshed is not necessarily always the major difference here. The Islamic Caliphate for example did not generally obliterate rival religions, for example, but rather discriminated against them with
jizya taxes and pressured them to convert. Zoroastrianism still exists even now, it was just marginalised into irrelevance. It wasn't like the Mongols.
The major differences instead are in
foreign support for the rebels and the
type of government the occupiers are trying to impose. Pakistan, at times helped by the USA, China, and others, has supported Afghan rebels for decades as part of a plan to extend its influence into that country, preventing a possible alliance with India which would encircle it. This is where the focus on casualties and military tactics is a bit misleading. The USA is obviously heavily restricted in permitted weapons/tactics, but the USSR was not, even to the point of poison gas attacks according to some reporting. However, escalations in military force were met with escalations in support for the rebels by Pakistan and others (the provision of Stingers in the 1980s and the "airlift of evil" and sheltering Bin Laden and Mullah Omar in the 2000s, for example).
Before 1998, Pakistan was officially aligned with the USA and protected by them. Since 1998, Pakistan has fielded a sizable stock of nuclear weapons, meaning any attempt to do something violent about this becomes politically impossible for obvious reasons (see also: North Korea, and Israel if you're on the opposite side of the geopolitical fence). If Iraq had actually had nuclear weapons in 2003, nothing much would have happened to them. Again, ideological issues don't really matter in this case; India would love to destroy Pakistan if they could, but it's no more an option than deleting the USSR was in 1985.
A very comparable situation exists in Northern Syria. Syria, Iran, and Russia obviously have no ideological problems with chemical attacks, indiscriminate bombing of civilians, mass execution/torture of POWs, and so on, but with NATO member Turkey giving massive support to rebels to the point of outright invading parts of the country to protect them all this is pretty useless and the war is an endless stalemate. Syria's state is obviously not just going to abandon their own country and run away, so the similarity ends there, but this is why "no military solution" absolutely applies here.
This is easily possible because of the second issue, the type of rule involved. In the past, empires were quite decentralised. A tribesman would have a chief who swore fealty to the king, and that was about it. Many of them were so remote they didn't even really pay regular taxes of any sort. Having one king as opposed to another was therefore often not as big a deal as it might seem.
This massively changes with modern states. Suddenly, who is in charge massively affects the rural tribesman, and the fact that this bunch of Pashto herders is on this side of the arbitrary Durand Line and not the other is massively important. Said tribesmen will probably prefer the Taliban and Pakistan to a central government run by Tajiks and Uzbeks and Americans. The state has no legitimacy outside cities and soon falls apart.
Regarding Britain, Britain never actually wanted to directly rule Afghanistan anyway, so it's moot. The plan was to have it as a vassal buffer state to block Russia from getting into India, and that worked. It's not really relevant to any of this aside from that British armies were sometimes defeated there, and sometimes successful.
As for China, Pakistan is their closest ally aside from maybe North Korea. They are far more likely to negotiate with the Taliban than fight them as a result of this. Remember the entire situation is a product of Pakistani foreign policy to start with.
