The level question really needs to be narrowed to what you want.
If you're a dialer, you want plumb elevation adjustment.
If you reticle hold over for elevation & wind, you want a plumb reticle.
If you shoot off a bench rest then you want the rest and stock level enough for consistent return to battery.
The action and rings and scope turrets may or may not be true to any of this, but I don't see how it matters.
And with level choices, be sure to use something you can see squarely -while pulling the trigger.
I'm a dialer. With this, I install a 'ScopLevel' and while shooting a box to test the scope I lock in the level true to elevation plumb. This level purely mounts to the scope, so it stays with the scope, forever set, even while I may use the scope for multiple guns over the years.

Consider that for a minute; I move the scope to another gun. I get behind the gun with comfortable hold off my rest (I use Harris bipods). I turn the scope in loose rings until lndicating level under this condition, and lock it down. DONE. I never have to mess with the actual level to do this.
I don't care about slight canting or misalignments of rest/stock/action/bases/rings/turrets/reticle. I only care that my crosshair intersection (my aim point) is true to intended POI -as adjusted via mechanical elevation internals.
That's me. I laser range, dial elevation, and hold off in inches for wind & mirage. My favorite aim point is a simple med-fine cross hair(no Hollywood). I could use a simple dot. Wouldn't matter.
Beyond that, to level the whole system, it seems to me the best time to address it is during stock bedding.
Then if needing plum reticle, you can just set a ScopLevel plumb to that. You can mount extra levels for the gun and rest.
The gun pictured is a Tubb T2K. I had set 12deg of cant in the gun(it's adjustable) because that was very comfortable. No matter, the scope was right.