[2023] Is there a way to see the achievements of my current run if I already had them in an older run?

You can look in your Steam achievements list for this game to see which ones you've got. They don't say what game name you completed them in, but they do give a date and time.  

I'm not sure I follow you - you can only ever get any achievement once ?!? I must be misunderstanding something!  

TealCat said: So I am looking for a way that will reliably tell me if something I did in my current save would unlock a certain achievement, independent of whether I had this achievement before in an older save game.

I am not aware of any such facility in any of our games, I'm afraid.