Hello there,

I'm having a problem with Continuity when using connected textures. Whenever I turn the setting on, wool, concrete, concrete powder, terracotta turn to the same texture which always is a shade of gray.
I can't find any errors related to Continuity in the game logs.
I'm running Continuity on Linux using X11 on an Nvidia card.

You need Colormatic for color features, which are not a goal of Continuity. Installing Colormatic will fix your issue.

I would then propose to add the info to the mod's pages that Continuity alone might break block colors and Colormatic fixes this, as this was not obvious for me.

Continuity does not break them. It just doesn't support them. Continuity never claims to support these features.

I'm confused. The colors I mentioned are the colors used in vanilla minecraft, no modded features.
As a user I would expect colors to stay the same if I install a mod for an unrelated feature like connected textures.
Do as you like, but I'd consider this useful information a potential user should be told about.