There is no possible way to achieve this goal without 4 happening though: or moreover, without it being possible.
Your prior 3 ideas all end up at "potential government surveillance of the people".
There is no way to implement verification like this without surveiling everyone, even if you don't plan to use the data - the possibility will always be there.
Yes, and this is one reason why we (Brits) have resisted Government ID cards for so long.
Those are separate issues though frankly. Unified government ID is efficient. You have it anyway, just as a morass of other forms of ID which contribute to the expense to administrate.
That's quite separate to "verify with your government ID" to visit a website having nothing to do with government services.
And it should be apparent that the lack of the former did not stop people asking for the latter. And they did ask for it.