You wrote: if we got into a 'space race' with, say, China
If? Seems to be well underway, both for who gets people back to the moon first (in this decade...) and possibly then who has the first base doing anything interesting or useful.
The first Chinese station bigger than Mir, the first commercial station, and the first Falcon 9 and Starlink competitors, will also have some bragging rights.
The military space race is well underway, from surveillance to communications to weapon platforms and how to attack and protect such satellites, to crew and cargo transport, etc.
And some day, Blue Origin, Virgin Galactic, or SpaceX, or someone will start regularly flying the huge backlog of rich people who want to go to space. By the time this gets going, there really may really be a space hotel (see commercial space station, above) for them to go to.