As someone who uses Omega daily, but mostly for playtesting and managing my real-life decklists, a feature where I could tag cards as “Owned” or “Not Owned” would be great.
A button I can click to toggle a grayscale effect on the individual cards in a deck seems like a quick and easy solution.
Love your program btw.
Use the “Favorite” feature. Mark the cards you own as favorites and that would serve functionally the same purpose. Another way to do it is simply the same way ygoprodeck.com handles it. You can manage your entire collection of cards on ygoprodeck and export as a whitelist (not a banlist). The whitelist defines what cards you own. Then in the deck editor you can filter by limitations → unlimited, limited, and semi-limited.
Lots of ways to do it.