ffmpeg -i input.mp4 -crf=20 -vf 'split[original][copy];[copy]scale=ih*16/9:-1,crop=h=iw*9/16,gblur=sigma=80,eq=saturation=0.9[background];[background][original]overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2' output.mp4
  1. Takes input.mp4
  2. Splits video into foreground and background
  3. Applies filters to background
    3. Scales to 16:9
    4. Blurs
    5. Desaturates slightly (range is 0-3.0, 1.0 is default)
  4. Composites forground and background together
  5. Saves as output.mp4

Uses a CRF of 20 which is very high quality. Change this to something more appropriate for your needs (higher CRF means lower quality and smaller file size).