I doubt you will find this in the bill, it will be an administrative detail, some faceless unelected bureaucrat will put it in, politicians will claim ignorance, but it will become a part of the system.
That is exactly the approach which will be taken and it is a very effective approach.
Barb C said in another post as I remember: “When they control your medical care they control you”.
When the only practical source for medical care for you or your family is the Feds, and you need care for yourself or a loved one, I predict you will check the box as having firearms. It will be a Federal Offense to lie on the form.
When asked to turn your guns in or face financial ruin, or lack of care because you can not afford the “high risk” pool, what will you do?
The highest risk I can think of is AIDS, the behavior which causes the transmittal of this disease is absolutely clear. But the group engaging in this activity is politically favored, Gun Owners are definitely not in favor with the elites. We will end up in the pool not them.