I don’t use subtitles much, but if I read the Help page correctly, local subtitle files need to be in the same folder as the movie, not in a subfolder.
Nope, to my experience “embedded” means also “muxed.in”.
The subtitles are within the same file as the video and the audio, but are still in a separate data stream.
That’s why the player can still enable or disable them.
“Burning” the subtitles into the video picture makes them permanently visible. (And also requires a lengthy and quality-diminishing conversion of the whole video stream)
Understandably, you want to avoid this option.