The projector is probably 16:9, it isn’t changing anything and isn’t really the problem. Plex must be aware of the black letterboxing area: it’s rendering the subtitles into it.
@Nebula, I did find this existing Feature Suggestions post:
Let us position srt subtitles to bottom of video - #5 by trogle
Consider using PGS subtitles when they’re available. Those would be composited into the image area.