Not sure why anybody would think the world won't work scientifically after Moshiach comes. Perhaps there will be more interference from Hashem but the fundamental rules of nature are not expected to change. We will still need to do hishtadlus to prevent illness just like we eat to provide nourishment.
Those who think Emuna is somehow contradictory to science have a serious flaw in their belief. Science works because Hashem gave it the powers. He can override it but he doesn't always do so.
There are many different שיטות on how the world will look after Moshiach comes. Your version may be one of them. However, there are definitely many that say that in the times of Moshiach there will be rules of nature that will be changed. For starters, the dead will awaken (tchiyas hameisim, which is definitely outside of the natural realm) as well as that all sicknesses will be healed - the blind will be able to see, the deaf will be able to hear and also anyone suffering from any ailment including but not limited to, cancer, heart disease, kidney disease, alzheimers, etc will be cured. So you can rest assured that those with COVID will be cured as well. According to this there will be no death and illnesses experienced any longer on this world.
I have no idea who is right and what will actually be. Nobody does. And it won't help us to continue to debate Teva vs Nes or how exactly the world will operate when Moshiach comes. We should just be zoicheh already for it to happen and we'll find out in real time.