@DVrandecic FYI the image is restricted

I've updated the description (mainly: it's only a problem in dark-mode browser/system themes) with new screenshots.
I'm not sure if the best solution is to either:

• create a new favicon that works well with any background? (We are currently using https://www.wikifunctions.org/static/favicon/wikifunctions.ico which I believe is derived from the SVG in https://commons.wikimedia.org/wiki/Category:Wikifunctions_logos )
• use CSS to switch between 2 different icons, e.g. @media (prefers-color-scheme: dark) might work?

In general: Ask a UI and/or graphic designer.
The simplest fix is probably doing what Wikipedia does, too: Put the logo on a white background. The more complex one is having a logo that works well as favicon on either background (Like phabricator’s). This will be tricky since the "W" is pretty flimsy (Same for Wikipedia’s W, thus their solution, I guess).

btw.: afaic one can use CSS for the favicon, but only if the icon is SVG (and thus the CSS will be the SVG’s CSS)

Suggest to split this in two issues just like one would do with a code-related issue. Solving that the outline looks bad has known fix (anti-aliasing and/or white background) whereas finding a favicon that looks less "W" like will be less trivial.

@Simulo Thanks for the nudge. I've split them properly now. I (should) know better than to merge semi-related issues; I blame semi-exhaustion! :)