VA and Medicare
Medicare and the VA generally don't coordinate benefits.
The easiest way to think of it is that if you have Medicare and VA, you choose which one you want to use at a given moment, but not both at the same time. You can go to a regular doctor and use your Medicare coverage or you can go to the VA and use them.
The only exception is when the VA authorizes care at a non-VA facility.
I find that most people who have VA and get Medicare and live in Southern California don't want to pay extra for a Supplement plan so they get the no-monthly-cost HMO.
People in Northern and Central California that have VA benefits and may be in an area that doesn't have a good enough no-cost HMO Advantage plan may choose to get and pay for a Medicare Supplement plan or they may just opt for what they can get for free and leave it at that.