Perhaps something like:

sudo modprobe v4l2loopback exclusive_caps=1 video_nr=99

ffmpeg -i /dev/video0 -i color-palette.png -filter_complex "[0:v] scale=-1:112 [scaled];[scaled]crop=144:112:(in_w-144)/2:0 [cropped];[cropped]eq=brightness=0.3:contrast=2[eqed];[eqed][1:v] paletteuse=dither=bayer:bayer_scale=1[gbc];[gbc]scale=-1:480:flags=neighbor[done];[done]format=yuv420p[v]" -map "[v]" -f v4l2 /dev/video99

With 4 color palette. Here is a base64 encoded png with the color palette I used.

iVBORw0KGgoAAAANSUhEUgAAABAAAAAQCAIAAACQkWg2AAABhGlDQ1BJQ0MgcHJvZmlsZQAAKJF9 kT1Iw0AcxV9TpVpaFOwg4pChOlkQFXHUKhShQqgVWnUwufQLmjQkKS6OgmvBwY/FqoOLs64OroIg +AHi6uKk6CIl/i8ptIj14Lgf7+497t4BQr3MNKtrHNB020wl4mImuyoGXtGLIMIIoV9mljEnSUl0 HF/38PH1LsazOp/7c4TVnMUAn0g8ywzTJt4gnt60Dc77xBFWlFXic+Ixky5I/Mh1xeM3zgWXBZ4Z MdOpeeIIsVhoY6WNWdHUiKeIo6qmU76Q8VjlvMVZK1dZ8578haGcvrLMdZrDSGARS5AgQkEVJZRh I0arToqFFO3HO/iHXL9ELoVcJTByLKACDbLrB/+D391a+ckJLykUB7pfHOdjBAjsAo2a43wfO07j BPA/A1d6y1+pAzOfpNdaWvQI6NsGLq5bmrIHXO4Ag0+GbMqu5Kcp5PPA+xl9UxYYuAWCa15vzX2c PgBp6ip5AxwcAqMFyl7v8O6e9t7+PdPs7wcH0HJ8UAGrtwAAAAlwSFlzAAALEwAACxMBAJqcGAAA AAd0SU1FB+cJCg0ZMBA5CWgAAAAqSURBVCjPYzS2VLZ20AgPidTRtGYgAjB+/HafgRTAxEAiGNUw qmHANAAAjvYFq/QT7j8AAAAASUVORK5CYII=

Inspiration: https://gameboymaniac.com/how-to-make-a-fake-game-boy-camera... https://www.bannerbear.com/blog/how-to-make-a-gif-from-a-vid... https://gameboymaniac.com/how-to-make-a-fake-game-boy-camera... https://www.bannerbear.com/blog/how-to-make-a-gif-from-a-vid... https://ffmpeg.org/ffmpeg-filters.html https://github.com/Lana-chan/webgbcam