Making Visually Lossless GIFs and Animated WEBPs

[Sound Master]

Which software can make the best visually lossless gifs out of videos? Also, how do I use rgb and/or rgba when making visually lossless animated WEBP files?

[pandy]

Which software can make the best visually lossless gifs out of videos? Also, how do I use rgb and/or rgba when making visually lossless animated WEBP files?

GIF can't be lossless, also it is highly questionable if 256 colors can provide "visually lossless" quality - of course you can create more than 256 colors (using GIF syntax or for example performing temporal dithering) but this is highly dependent on your GIF viewer capabilities.

Quality of GIF depends mostly on color quantization quality - error diffusion can help but color selection is most important - there is not many good color quantization algorithms - my favorite are NeuQuant and SColorQ - also color space can be important - technically you need algorithm matched with human vision - this is similar area to automatic subjective image/video quality measurement - all methods are still very simplistic when compared to human vision.

https://bisqwit.iki.fi/jutut/colorquant/
https://www.imagemagick.org/Usage/quantize/

This may be also interesting for you https://bisqwit.iki.fi/story/howto/dither/jy/ - more about dithering topic .

And short reply - IMHO GIF is not even close to be visually lossless.

About WebP question... did you tried to read:
https://developers.google.com/speed/webp/faq
https://developers.google.com/speed/webp/docs/using

?