As per the title - I'll try and give my personal and professional experience, without providing any specific medical advice (which is fraught with risk over the internet, without being familiar with your medical history).
I have been working as a specialist General Practitioner for the last 5 years, and am currently working in a COVID screening clinic in Melbourne seeing all the lovely coughs and colds.
Not sure I 100% understood what you were asking, but I'll try to answer the best I can. Before these COVID lockdowns I used to go to the gym everyday after work listing heavy compound weights (or doing light cardio on my off days) for around 1 hour. It helped that the gym was literally next door to the practice so I didn't find it a drain on my time at all. Obviously that's gone out the window now with the lockdown restrictions in Melbourne (and I'm still personally hesitant to go back even though gyms are opening back up again), and I definitely could stand to lose a couple of kilos from the effects of boredom eating.
In fact, I genuinely believe and advise my patients that exercising is the best investment in their time because it forces them to organise their schedule better, improves mood/sleep, improves mental clarity throughout the day, improves capacity for physical exertion (which helps in activities of daily living) and of course maintains cardiovascular health (the main cause of morbidity and mortality in our Western society).
Having that energy, mental clarity and positive outlook on life can only help with productivity at work, and I would strongly encourage investing your time in daily exercise if that's something you're hesitant about.