Let’s make a list of tabletop RPG rules and settings useful for running/making astronaut missions.

Definitely Astronat RPGs/Settings

• Apollo 47
• Holdfast Station
• Jovian Despair
• NULL_SPACE
• Orbital 2100 (a setting for Traveller/Cepheus Engine)
• Orbital Cold War (a setting for Cepheus Engine)
• Outpost Mars (a setting for Cepheus Engine)
• Pioneer (upcoming astronaut RPG by the people making Traveller)
• Sixty Years in Space
• Void Above

Can be used for Astronaut Missions

• cramOS. Robotic RPG, which could fit playing as a group of rovers (like the Curiosity/Perseverance Mars rovers) or robotic astronauts (like NASA’s Robonaut)
• Eclipse Phase, specifically a Reclaimers salvage/orbital debris cleanup campaign.
• GURPS Transhuman Space. The rest of the solar system is ripe for astronaut missions.
• HARDCASE. Near-future gig economy on a space station. Salvage jobs (like the Maria Seraph) help this game somewhat appropriate for astronaut missions.
• Jovian Chronicles. A hard sci-fi mech game in our own solar system. A campaign about Explorers, Spacers, and Technicians (rather than the mechs) using a Gritty or Adventurous Reality-Distortion level fits astronaut perfectly.
• Mothership. A game about the stress and horror of working in outer-space. A mission for Teamsters and Scientists would work perfectly as an astronaut mission - just hold the spooky crab monster on the side.
• Mutant Year Zero. Specifically via the Ad Astra expansion/campaign setting, which is all about survival and discovery in our mutated solar system.
• Orbiters Local 519. A game of salvaging space derelicts. Can work well for a darker, dangerous reimagining of Planetes-style space garbage collection.
• Shadows Over Sol. Mostly space-horror, but frequently goes all-in on astronaut missions.