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I think the problem might just be that macOS doesn't properly update the amount of available disk space. At least since the introduction of APFS, this all a bit wonky.
Another thing to consider is that Time Machine does save local backups right on your main drive as long as it doesn't have the opportunity to dump stuff on an external drive. (This is usually not really a problem as the local backups get cleared at the latest when you really need the space.)
Try rebooting your Mac and/or hook up your external Time Machine drive (if you have one and haven't done that already) and check the available disk space then. In my experience, the space get's cleared then and the amount gets properly updated.
What made me think it was a Steam issue, rather than Mac, is that downloading game files made the HD space go down but deleting files didn't make the space go up. And I was able to delete other, large files on the hard drive that were immediately reflected in macOS's report of the hard drive's capacity — only Steam deletions weren't being reflected. Weird.