I couldn’t find a more updated source on this, but this post gives you an idea of what mana efficiency does.
If this formula is still correct, then none of your formula’s are correct.
Additionally, I would think that the rest of the calculations behave similarly to how they work for damage, but I’m not sure. But, with this information, you should be able to test that theory with concrete values and figure it out.
I have a guess of what it might look like, but I don’t want to speculate.
You could also look in the game guide there might be more information there.