The original video plays in the correct aspect ratio with bars on the side. When I expand it to full screen, there are bars on all sides, but the aspect ratio is still correct. When I play that video through Plex, it stretches the top and bottom of the video and ruins the ratio.

Does anyone know how I can fix this (with re-encoding)?

I don't mind if there are bars on all sides like in picture 2, I just want the correct aspect ratio.