1st herrscher: Can construct anything the user understands completely out of thin air.
2nd: Control over space and time.
3rd: Control over electromagnetism
4th: Ideal fluid manipulation. (In my understanding she manipulates ideal fluids, in this case air currents. With no viscosity and friction. Meaning her wind could move with 0 energy loss. So she is able to make continental wide mega typhoons and her wind packs much more punch.)
5th: Molecular deceleration. Can reach absolute zero. (Making chemistry impossible, you turn to goop.)
6th: Matter control. Mainly restoration and annihilation.
7th: Molecular acceleration. (Can make any form of matter heat up to any level. Only depending on the herrscher's strength.)
8th: Can create inescapable illusions that can last eternally. (Dying in the illusory world translates to physical death.)
9th: Could control gravity and even create pseudo black holes that have an event horizon and time dilation.
10th: A collection of herrschers that could control a weaker version of the powers of the other herrschers before them.
11th: Nigh absolute control of honkai energy and can manipulate any kind as well. Only 2nd to the 14th in honkai manipulation.
12th: Self aware lethal virus that could infect organic and inorganic things. I.e. Computers, AI, software, etc.
13th: ???
14th: Absolute control over the honkai. Basically omnipotent if the gestalt will of honkai allows her to use infinite amounts of honkai energy.
(I'll update this whenever new herrschers appear. Just so other people can understand just what their powers are. They don't control elements or anything. They control a concept, that's why if they are allowed to understand it. It is literal hax in a universe like honkai, that follows physics to a certain point.)