The frustrating reality is that K-dramas get licensed to different platforms depending on your region and what deals each service negotiates, so there's no single app that has everything. That said, the tools people mentioned work - I'd second JustWatch since it actually does pull from most of the major ones and shows you exactly where each title lives right now.
Beyond that, if you're serious about binge-watching without the constant switching, consider whether a couple of the services you're already paying for might have more K-dramas than you've discovered yet. Sometimes people don't realize Netflix or Disney+ has a whole catalog they haven't scrolled through because the recommendation algorithm isn't pushing it at them. Worth poking around the "International" or "Drama" sections before signing up for yet another subscription.
The real move though is just accepting you'll probably need two or three services max if you pick the right ones for your region. Where I'm at, Netflix and one of the smaller ones cover most of what I'd want to watch, so I rotate which month I'm subscribed to what. Sounds annoying, but it's cheaper than keeping five active at once.