Cardio workouts come in many shapes and sizes. In fact, any workout that puts some strain on the cardiovascular system can be considered a cardio workout. That said, people usually associate cardio workouts with exercise classes, whether it's sweating on a Peloton or jumping around in a Zumba class.
For anything jumpy, we'd recommend well-cushioned shoes, such as the ASICS Gel-Kayano 29, which is a running shoe but stable enough to provide lateral support for jumping. Most running shoes can be used for treadmill training, although we'd advise against max-cushioned running shoes (e.g. New Balance SuperComp Trainer) as they can be pretty unstable on the belt.
If you're really keen on putting as much effort as possible into cycling workouts, we recommend using dedicated cycling shoes, or if you're riding a Peloton, the best shoes for Peloton. These will help you make the most of each revolution by connecting your feet to the peddles, which cranks up intensity quite a lot.