Commenting more or less in the order in which you brought up the issues:
I do admit I’ve never needed to peek at this particular detail, but I’m not sure MusicXML stores information about what font is used on a score. Feel free to correct me if I’m wrong.
Still, even if it did, the “somewhat established interchangeable format regarding music fonts” you mention is actually SMuFL, which was created in the run up to Dorico’s development, and hasn’t been adopted by Sibelius or Finale. This means that the fonts that one software uses aren’t compatible with the others (not in the sense that the glyph mappings are different). Whatever limited immediate compatibility there might exist between Sibelius and Finale’s fonts rests on loosely adopted unofficial practices regarding glyph mapping in musical fonts.
And Dorico reads all correctly installed fonts in your computer. You’re most certainly looking at the Music Fonts menu. This menu will be populated exclusively by SMuFL fonts with available metadata. To force Dorico to use other kinds of fonts, you’ll have to look to the menu just below and set the adequate Font Styles.