The base is 0.480” on the Swede. Many American cartridges are built around 0.473” based 30-06 or 308 action length....but does this matter?
You are confusing US vs European and an apples an oranges sort of way.
Yes, the bolt head has to fit the case. How much extra a US 06 class bolt head has vs the dimension of the 6.5 x 55 I do not know (I can check)
If the gun is designed for 6.5 x 55 then its not an issue. It will have the right clearance for a .480 base.
If you are converting a US gun TO 6.5 x 55, then it may or may not work.
I did it with a 7.5 x 55 Swiss, I had to open up the 30-06 base sized bolt head a bit.,
Easily done with the right touch and some lucky (you only get one mistake! - and no way to practice realistically)
Any ammunition that is 6.5 x 55 will have the 6.5 x 55 bolt head size no matter where it is made.
It sounds like you are getting mixed up with US heritage vs the European in base size who have their own and don't care (nor should they)
So while a great many cartridges in the US are derived from the 30-03/30-06, max nix.
The US cartridges have settled on their base sizes and tend to accommodate (if not 100%) the existing family of cartridges size wise.
The loadings are a different story due to the history of the 6.5 x 55 and what level it can be pushed to in what gun, but has nothing to do with the base size.
The 6.5 x 55 base may fit a 30-06, but its going to be quite tight and even if it just does, mabye not good ejection. You need a bit of extra openness to work right.
My 7.5 is tight, but I had it where I wanted it and its a single shot bench rest shooter, so I am not concerned about feeding.