After a lot of head-scratching, experimentation and help-asking, I found an unsatisfying workaround by doing this in my PHP script:
$output_from_Argos_Translate = iconv('Windows-1252', 'UTF-8', $output_from_Argos_Translate);
As you can see, I’m converting it from ‘Windows-1252’ to ‘UTF-8’, because for some reason, Argos Translate appears to output as ‘Windows-1252’ for me instead of the expected UTF-8. This is in spite of me running this in a cmd.exe which has my standard chcp 65001 > NUL line in the beginning, which instructs cmd.exe to use UTF-8 as the “code page” (archaic term).
‘Windows-1252’ is not something which I have actively picked, but is set in some sense by Windows for my language, so maybe/apparently, Python or Argos Translate gets confused by this and thinks I wanted that charset instead of UTF-8?
So in other words: I have it working on my specific machine, but I would rather have the issue resolved, assuming it’s something within your control, maybe by adding an optional “charset” parameter or something like that?