I have to mention this because I often forget: raw onion is a completely different creature. It takes zero minutes to cook—you just chop and serve. But the sharp, tear-inducing bite is its own beast. To tame that bite, you can soak raw slices in cold water for 10 minutes. That’s not "cooking," but it’s a technique worth knowing.
Honestly, I think the real question isn’t really about time. It’s about what you want the onion to say in your dish. Do you want it to whisper sweetness? That’s the slow caramelization. Do you want it to shout "I’m here!" in a salad? That’s raw. And if you just want it to be present without a fuss? The five-minute sauté is your ride.