>The space race was to get to the moon.

That's either revisionist or ignorant (likely the latter, looking at cheap memes). The term was coined by American journos in the early 50's, and the actual events started in 1955, very publicly. And objectively speaking it never ended until the USSR crashed.

You should probably read something on the Soviet space program (starting with Rockets and People, for example), and the US one while you're at it. The Soviets didn't went all in on satellites. They simply returned to the original ideas Korolev & co had long before Sputnik ever flew, namely LEO modular assembly tech followed by manned circumnavigation of Venus (before the surface conditions were known) or Mars (after that) as a meaningful first step in deep space exploration. Which was pretty pragmatic and long-term thinking, although it's hard to say how realistic it was politically: they would have finished by the late 80's at best and securing the funding without propaganda-worthy progress wasn't a given. Regardless, they succeeded at actual LEO colonization, which was presumably "not space race" (I'm sure Space Shuttle/Freedom being a massive failure and NASA seeking Soviet expertise after the crash has nothing to do with that framing...).

Lunar missions, let alone single-flight ones without modular spacecraft, were a practical dead end and a distraction, the engineers understood that perfectly. The party however got successfully baited by JFK's advisors into the race they couldn't win because they still needed to close the "reverse missile gap" after the US panicked and closed the actual missile gap they imagined existed by building a ton of Titan IIs. The Apollo people were also in perfect understanding that the program had no practical followup and only existed for novelty, see anything written by Chris Kraft and Gene Kranz who were actual participants. STS was a colossal blunder and a setback as well, in practical terms, and it was obvious before the first flight.

The race was never limited to manned missions either. For example most of what we know about the Solar System comes from the JPL, which is hugely underappreciated. The Soviets only succeeded with Venus missions.