Get browser's default accent-color

And what accent color is set for you? I think if your UA does not set any value, it will be auto as specified in documentation

Open browser dev tools, ensure Browser Styles are shown. Inspect element, at least for my Firefox there is no accent color applied for that input

I don't think this is going to work anymore, and the complexity is off the scale for something so simple.

https://github.com/JoelBesada/accentColor

Try to study this script.
This is done by calculating the dominant color of the site's favicon, which generally gives the expected results. The format of the returned color is 'rgb(R, G, B)'.

directly extracting the Hex/RGB of a system auto value is intentionally restricted by browsers for privacy. The best workaround is to use CSS System Colors so the browser handles the matching automatically, or to use a library like accent-color (referenced in the comment in your image) which uses a complex "snapshot" method to guess the color.