What browser are you using? I just tried this with a 0x00 to 0xff linear gradient ( https://www.imagemagick.org/image/gradients/linear_gradient...., duplicated so I have two frames) encoded to MPEG levels (16 to 235) 8-bit h264.

    ffmpeg -r 30 -f image2 -i linear_gradient%02d.png -vcodec libx264 -preset slow -crf 22 -pix_fmt yuv420p -start_number 1 -vframes 2  linear_gradient.mp4

Firefox stretches it to 0x01 to 0xfe, and introduces obvious banding in the process. MPV does the same thing, although it has an optional debanding filter. The black and white levels are only a single unit off from the original, so I doubt I'd notice in real video. The banding is a much bigger problem (solved by 10-bit color spaces), but GIF has more banding in general use.