Why do the Greek font characters I’ve written in a Word doc not convert to Greek in a PDF doc but convert instead into their english transliteration?

At a guess, because you have used a non- Unicode font in the Word document, so the actual characters used are ASCII.

There was quite a lot of infrastructure available 10 years ago for converting between ASCII fonts and Unicode. Not sure there will be as much now.

If your source document used a Unicode font, then it’s puzzling. Transliteration is above the paygrade of PDF converters.