Without going into the weeds on the exact developments in space rocketry, as that's outside of my lane, I would argue that the reason that the Germans were ahead in high-altitude rocketry at the end of the war was because they were the only folks desperate enough to put resources into that area. The Americans and Russians didn't advance much that way as it was sortof irrelevant.

Take three names: Goddard, von Braun, and Galkovskiy. All three well famous for their high altitude rocketry work. Goddard started it all, von Braun generally sorted out ballistic missiles and later much of the American space program, and Galkovskiy was part of the Sputnik team.

Obviously, there are many competing tasks requiring limited resources such as a scientist's man-hours in a war. Inventions by Goddard which showed up in WW2 include the Bazooka anti-tank rocket launcher, and variable thrust rockets for the US Navy to launch heavily laden aircraft from Carriers. Galkovskiy's name is prominent in the development of the Katyusha multiple rocket launcher, known as Stalin's Organ. Both of these chaps were involved in the making of tactical devices, things which could (and did) have a significant impact on whether or not battles would be won or lost. If the Americans wanted to bomb Germany, they simply put together a few hundred B-17s, and flew over. Maybe they could use one of the B-17s with one of them "gadgets" taking up so much of the research budget in New Mexico. There was no need to waste Goddard's talents on big rockets, the ability to punch holes in panzers was far more critical to US success. The Russians (who, in fairness, had much more of a tactical than strategic air force) may well have decided that the ability to drop explosives on Berlin was needless: They could simply flatten the German soldiers between them and Berlin and then sit on the city. Which they ended up doing. Katyushas were very good at the whole 'flattening' thing.

The Germans, though, put their effort into the the strategic, not tactical, problem of getting explosives to the UK or US. There was no chance for them to do it by air or sea. And things on land weren't going fantastically well. So they put their rocket gurus onto the big rockets like the V-2 in the hopes of the war-winning wunder-waffe. Of bugger-all use in WW2, really, but the technology was going to have great peacetime use. Both the Russians and Americans understood this, so when they took their scientists off the task of 'build things to defeat the enemy', they realised that the wrong turn the Germans had made in WW2 was the right turn for the Space Race, and that their work would be needed.