How do I manage favicon?

Simply by using WordPress standard method:

Thank you, Matthias for screen capture, it saved me some time changing one website language to english 😉

If you want to change the icon dispayed by Google in mobile search, you can read this good post from James.

In addition:

WordPress > Appearance > Customizer

If you don't see that menu item, switch your theme from "Twenty Twenty-Two" to "Twenty Twenty-One", or even better, install "theme "Intentionally Blank".

Please note: with Oxygen installed, the activate button in the themes screen looks disabled, but it's working fine.