Can't find any option to add another game as a Category Extension (in main game setings). Do I also need to be a mod for CE game?

You can request a Category Extention in a Support ticket under "Add a new game to Speedrun". Just explain in the description that it is a cateogry extention. And put " Category Extention" as a suffix in the game name.

I'm not sure about the requirements to add a CE. But maybe they should only be added if there's a bunch of miscellaneous categories on the main board. Also that you should explain why you need one in the description of the ticket.

And if there is already a board for CE, but main board doesn't have direct link to it?

Then submit a Support ticket under "Change an existing game or series", then "Change the type of an existing game", then check "Category Extension", and then choose the base game as the main board.

Cheers for help