if you get sick from the vaccine,will your medical insurance cover it

Of course your medical insurance is "still good." You would pay any applicable copay/coinsurance. Worst case, you can also end up in the ICU by refusing vaccination.

Actually, worst case is you don't get the vaccine, you get covid, have it for a long time, it mutates in you, gets more deadly, and you pass it on to your loved ones and the rest of us.

It would be insured like any other Illness but the risk of serious complications are minuscule compared to the risk of Covid. It is very safe and your insurer wants you to take it because it will drastically reduce your risk of getting Covid which is very expensive for them if you end up in he hospital.

Better (funnier?) question would be: If you don’t take the vaccine and die, is that considered suicide, and does that affect life insurance payout?

My dad always says if health insurance wants to give you something for free it’s probably a good idea and if life insurance asks if you do something it’s probably a bad idea.