I’ve often heard that there was a specially recorded song by The Carpenters (usually in the context of jokingly complaining “why The Carpenters? The aliens are going to think we suck”). But it’s not on the list. Is it an urban myth? Were they on a different spacecraft?

After a quick Google - they did a song about sending a song into space. Then they did a weird-ass TV thing about sending that song into space. But as far as I can tell, no Carpenters song has actually been sent into space.
(yeah yeah radio waves whatever. You know what I mean)