Whenever I select a dark mode theme using the mod, the F3 screen changes as well.

F3 screen without any dark mode theme:

F3 screen with the darkest dark mode theme applied:

why dont you just use a texture pack?

Texture packs don't support all UI's like dark mode everywhere does. This mod combination also messes up the hotbar and WTHIT tooltips. I made an issue over there, not sure which mod would need to change to resolve this (or both) TeamAOF/DarkModeEverywhere#1

I guess I should add, please don't open issues on other people's mods for compatibility with this mod. It was never intended that this mod works with everything, and it probably never will. Creating issues on other repos mostly just wastes people's time.
There issue here is that the backgrounds needs to have a default color(unlike normal rendering), which messes the dark mode color logic up(since it gets added on top).