Normally business use is "similar" to commercial insurance. But it appears that your insurance only covers while driving back and forth while working, but (excludes) if you have people/patients in your vehicle.
See the difference between the 2 is that if you have an accident, they will cover you, but if you have a patient in your vehicle, then your insurance could be on the hook for injuries, thus they will (not) cover you.
This BS that your employer states that your insurance will cover this is just BS. If/when you were to have an accident with a patient/co worker is in the car, then you don't wan t to find out that your insurance denies due to being not covered or in other words excluded. The patient can sue YOU, the driver/owner of the vehicle that caused their injuries.
So, unless you can get a letter from the (company) not your boss stating that (if) your insurance does not cover you, then they will pay for any damages/injuries. Or, better yet, let them provide you with a company vehicle that you use, so it will be the companies insurance and not yours.
You can change your insurance from business to commercial, but the cost maybe much much more. So you can then ask your employer to pay you the additional cost to cover you.
Your employer in "effect" has asked you to be a taxi driver. They need to hire more employees that drive their own vehicles vs using the current and having other employees drive for them. They have what they call (real) taxis, or Uber or Lyft for that reason, so let them pay them to drive them instead.
Don't do this and make sure that other employees do the same, thus they would have to either let everyone go, or find other solutions