Starship has absolutely not done cryogenic fuel transfer demos. They have attempted to do so, but have so far not succeeded. And they are a long way of having two ships in orbit and transferring fuel between those.

Also the ISS has not been refueled in terms of rocket fuel, because it has no rockets itself. It relies on attached capsules to boost the orbit. These capsules bring their own fuel and engines.

However I agree it should be possible in principle and will probably be demonstrated somewhere in the next couple of years.

But the point isn’t that it technically can’t be done, the point is it can’t practically or economically be done. It isn’t as simple as putting some kind of big storage up there, slowly fuel it up and when it’s full, launch your mission and stop by the gas station. This is a much too simplistic view. First of all, how are you going to get the big fuel depot up there? That would require multiple missions and in orbit construction on a large scale. Something that is expensive and takes a lot of time. Second of all, these are cryogenic fuels, as the name suggests, these need to be kept very cold. But space is really cold right? No actually, the distance from the sun is what mostly governs the temperature, so orbit around Earth is still pretty hot. It does get cold in the shadow, but in the sunlight it’s hot. That’s why the ISS for example has huge radiators, because they need to get rid of that heat. And since radiation is the only way to get rid of heat, it’s pretty inefficient. Third of all, storing cryogenics is very hard, to the point of impossible. For rocket launches the fuel is stored for only a couple of weeks and needs a huge amount of power and infrastructure. And it requires continuous venting as to not build the pressure to dangerous levels. Getting an infrastructure like that going in space would be very hard if not impossible at this time. Best we can do is just let it vent a lot and use that venting to regulate the temperature. But that means losing a lot of fuel all the time. So if the refueling missions don’t get there fast enough, so much fuel would be lost, there is no point.

All this boils down to either a huge infrastructure project on orbit, on a scale and cost we’ve never seen before. And/or depending on how well that turns out, dozens of launches within hours of each other. That means a whole bunch of rockets, huge amounts of fuel. The logistics and timing would be insane and the amount of infrastructure needed for something like that is insane as well.

Falcon 9 is breaking records with their launch cadence, but they are only doing on average 3 launches per week. And that’s a much smaller, much simpler rocket by comparison and includes re-use of a lot of the rocket. For something like Starship the scale goes up by a lot, requiring a lot more to get to the same level. And if you want to bring as much fuel as possible up there, re-use becomes a lot harder. Keep in mind that it took SpaceX a very long time to get Falcon 9 to this level. Starship hasn’t even done a single orbit yet, on paper it is an impressive machine, but it will take a very long time and huge effort to get it to the level of Falcon 9. And even if you do, it’s not good enough, what’s required is something on the order of 18 launches within a few days.

And this isn’t something far fetched, a lot of people have done the math and it just doesn’t work out. But as the reasons behind the current approach are political and not technical, pointing out the technical impossibility isn’t really going to change anything. And so many people have drunk the Musk kool-aid, believing his wild and unsubstantiated claims. Starship is hella impressive, but the thing ain’t magic and it also doesn’t exist yet.