Tonguez
A suffusion of yellow
It is the year 2500. The solar system is teeming with colonies, from terraformed Mars to the cloud cities of Venus to the asteroid mining colonies and beyond. It is all possible due to the Thread Network of superdense filaments linking colonies in an ever expanding transit system wen. But suddenly, the Lucust Fleet arrives, attacking humanity (including augmented humans, uplifted animals, sentient machines and other transhuman beings) and nearly causing our extinction. Only a terrible gambit that causes a massive solar storm defeats the Locust Fleet, but at a unimaginable cost. Most of the utopian technology of the solar civilization is destroyed. Between that and the depradations of the Locust Fleet, the solar system is a post apocalyptic hellscape. The Thread Network remains, however, since it is built on a function of physics, not technology. Anyone who can jury rig a space worthy rocket plane into space can traverse the colonies. But who knows what they will find in the ruins?
See? Straight up post apocalyptic setting with space travel not just possible but a central conceit.
Look at examples like Fading Suns or Crawfords Stars Without Number both have a similar spacefaring civilisation suddenly wrecked but now recovering. Both are space opera/sci fi but I dont consider them apocalyptic and really if theres enough tech to juryrig and fuel a rocket plane is there really post-apocalyptic scarcity?
Cowboy Bebops an interesting example too since although Earth faced an apocalypse its surviving underground societies are doing okay due to trade with off world colonies. Which is my point about interplanetary travel removing the burden of survival level scarcity.
As to the abandoned mars colony - have you seen the Dr Who episode “Smile”? The Tardis lands on an off-world Earth colony which is empty except for millions of nanobots that maintain it, along with robotic avatars that interact with the pair via emojis. They also discover human bones …(I’ll leave it there incase spoilers)
Anyway its a good episode with a mystery to be investigated and all the standard tropes of Dr Who including space travel,but despite having all the features described in your example its not post-apocalyptic.
really Metamorphisis Alpha maybe the only example of post apocalyptic space ship listed so far, but even then, as far as the inhabitants know its a proper world, so in that regards its kinda like The Dragonriders of Pern which initially presents as a fantasy until you discover the twist
anyway thats just my opinion,,I’m happy if others have different opinions of what makes it into their post apocalyptic setting