In practice, I expect much of the answer will end up being "militarize space a whole bunch more".

I don't think anyone's expecting anyone else to actually abide by all those space-related treaties if there's another Great Powers war. Which, this century, means only one pairing: the US and China.

More surveillance, satellite kill vehicles with perhaps a little plausible deniability, dark, redundant GPS and comm sats, maybe some new, secret constellations at novel orbital heights for when all that debris gets spread around the lower orbits and screws everything up... maybe not actual space-based ground-targeting or anti-ICBM weapons, but then again, countries do cheat on treaties.

I'd encourage anyone bothered by this post (evidently, someone was) to check out the stats on past and upcoming SpaceX contracts. The overwhelming majority are the US military and NASA, and the US military's share isn't far behind NASA. Seems clear to me the smart money is on "same stuff, but more of it" if they bring costs down even farther. And I'd say the US military's got more room in the budget to quickly put together useful payloads than NASA does, if the prices drop, which narrows it down to "mostly more military stuff". And especially if Starship gives them the ability to put large payloads in higher orbits on the cheap. I bet they've got filing cabinets and skunkworks warehouses full of shit they'd love to build/finish and launch as soon as the costs work out.

But maybe I'll be surprised and military launches will remain about the same while StarLink competitors and elementary school students launching cubesats will eat up all that new, cheaper capacity.