Using ffmpeg to add height (as black bars) to video file without quality loss
You'll have to manually set encoding parameters.

ffmpeg -i input.mkv -filter:v "pad=3840:2160:0:280,setsar=1" -crf 18 -preset faster -c:a copy my_output_video.mkv


The CRF option sets the tradeoff for size/quality. Lower values produce better quality but larger files. The preset will increase speed, but for same quality, the file size will be larger.

The setsar filter has been added as a precaution in case your player reads the SAR stored in the file and stretches the video based on that value.