He who is your best friend today may not be your best friend tomorrow. I'd say your "best friend ever" is the best of all time. Your "best friend" is simply the best at that point in your life.
"Best friend of all" might mean "of all time", but it also might mean "of all the people who are best friends to other people, you are the best out of all of them".
"Very best" emphasizes that there is not an unspoken proviso affecting "best" that would otherwise make it truly less than best.
But oftentimes in many languages we tend to intensify absolutes, usually but not always colloquially - mostly because we use absolutes in a sense that isn't absolute. For instance, I got pizza yesterday, and after eating a couple of slices I told myself 'This is the most I can eat!' - and then proceeded to eat a couple more slices. And then I told myself, 'This is the absolute most I can stuff my face!' ...as if there are different levels of 'most', despite it being a superlative and so an absolute.
I'm not the only one, people speak daily of things being more perfect than other perfect things and tasks being more complete than other tasks they've really finished. I couldn't tell you why we do it, but superlatives don't always have a superlative meaning, so 'very best friend' is, while semantically confusing as per what standardised rules say, completely idiomatic.
Certainly a good example haha. I'm guilty of using literally in a figurative sense myself, but it's very convenient because it's a lot more forceful than equivalents like 'practically' or 'virtually'. I'd react in a more emphatic way to 'it literally killed me' than to 'it virtually/practically killed me', but maybe that's just me.
I couldn't tell you about the Swedish, but in English, at least to me, 'absolute' is sort of the absolute absolute – so if you called me your absolute best friend and someone else your best friend of all, I'd feel that you consider me more of a friend than you do the other person.
Then again, like I said earlier in this discussion, we tend to ❤❤❤❤❤❤❤❤ our absolutes a lot, so it's really a subjective difference.