What additional exercises are recommended by clinical studies to promote physical health for people have a sedentary occupation, but who already perform weight-lifting and cardio exercises on a regular basis?
Mayo Clinic recommends 150 minutes of moderate/aerobic exercise weekly - so 30 minutes for 5 days. "As a general goal, aim for at least 30 minutes of physical activity every day."
It sounds like you already do a good job at including physical exercise in your daily routine, so that's great! If you can, try to do those activities with a workout buddy too. I learned in my stress class that interpersonal sports (such as games where you work with teammates) also have good health benefits... (Sorry I don't have the source on hand right now.)
If your concern is "medical health," then consider your diet and other aspects of your lifestyle as well; it's not only about your activity. But because you asked about exercises, I won't go into those details for now - I'm only recommending that you think about other factors as well for your health. For example, are you interested in deep breathing exercises for mental health?
You can also think about your health while you're sitting at desk the whole day: how is your posture? Would you consider standing at your desk if it can change levels? How is the air quality in your office?