How to make a "virtual category" in WordPress?

Question

Taxonomy

Hello!
I've been scratching my head over this problem for the second day, I feel that the solution is somewhere on the surface, but I can't get to it.
Essence:
The plugin, under certain conditions, adds meta-data to posts, such as colors.
The same plugin should form "virtual categories" (do not touch the theme files, including functions.php, just the plugin). Those. when accessing /color/red, the "category" page (standard template) should open with posts with a red meta field.
How to "trick" WordPress into giving it a selection of these posts instead of displaying a 404?