Hi Kalsta!
No, it was unfortunately not a permanent fix. But I don't have as much as half of them grey. Suddenly today my Yahoo mail icon got its color back after being grey for ages. And suddenly today my two NRK icons (Norwegian broadcaster with news and TV) have a logo for NRK Sport (!?). Very strange since I hate sport and never ever have visited NRK Sport. Those icons are living their own life, for sure.
I did have more or less the same problems as you. It was fixed at first, but then started to get grey again and with disappearing logos. But never as bad as before. I did not try to fix it several time, I just gave up. Why? Because I have a bigger problem that I have no idea how to solve. When opening a new tab, it often freeze Safari for a while (like roughly halv of the time). That is extremely annoying. And on top of that I have to crash Safari several times during the day because everything freezes. I can't remember exactly, but when pressing "report" to Apple, I get this crash report saying something with too many stacks or something. And I can't play movies or TV-show from a specific Norwegian site. Safari just can't load the movies, even though that the site says that for Mac, Safari is the best to use and should work as long as it is updated. But it doesn't on my machine, so something is wrong and I have no idea how to fix it, not even how to search forums for a fix. When visiting that site, I have to use another browser. And I don't like them, not at all. I love Safari, but hate all the problems that I have with it. And I forgot to mention Safari is really slow because of Adguard. I have tried several adblockers, either they don't work to get rid of the GDPR warnings or the are slow as Adguard. Everything just works perfectly when using the Opera browser. I want Safari to work just as good, but yes, I sort of have given up since I'm not a computer engineer or something.
I'm now downloading the Big Sur update, I hope that will fix some issues with grey icons, freezing problems and such. We'll see. I don't have too high hopes though. But maybe, since I have reported a lot of the crashes to Apple, they might have fixed things.