In a document I’d like to gather all text colored red, say. I can find instances one by one using Find by Formatting, but how to I select them all so I can copy and paste?
Scrivener doesn’t have a tool to do this automatically. You could set up a split editor with the new document you’re pasting to on one side and use Find by Formatting in the other to jump to each instance, then copy and paste into your paste document. Ctrl+Tab cycles between the binder and each editor; if you close the binder, it will just move focus between the two editor splits. Ctrl+Shift+F3 will jump to the next instance of the formatting.
You could also set your paste-to document as a Favorite (via Documents > Favorites > Add to Favorites), then use Edit > Append Selection to Document (also available in the editor context menu) to add each instance of the formatted text to the document. Assigning the document as a favorite will keep it easily accessible at the top of the list.