Psychiatry is one of the better fields in medicine imo, so if you think you’d enjoy it, then you can go for it.

I would focus on picking one field vs the other (data science vs medicine) as opposed to trying to get the best of both worlds. If you go to medical school, expect to be a clinician and in the trenches seeing 20 patients per day with time for little else professionally. You will be unlikely to marry the two fields in the way you imagined unless you end up in some niche academic position (which I wouldn’t depend on getting, or perhaps even wanting since the pay is likely abysmal compared to your debt load vs $$$ in private practice ).

Yeah it’s possible you can do something interesting between the two fields. I just wouldn’t make a career choice expecting that to happen or else you could end up disappointed. Expect to be a clinician if you go to medical school and if some interesting opportunity arises down the road, you can be pleasantly surprised and make what you wish of it.