Question for geniuses - Are you?

Restore on mouse leave means it will return to it's prior (non-hover) state. Try deselecting that box.
If that doesn't work, duplicate your hover state as the visited state than use a trigger like this:
Change state of ButtonSuche to Visited When the user hovers over ButtonSuche.

I think it makes more sense to use button sets w/ states than hotspots to manage the visual changes to your objects. Check out the attached demo file to see if it helps. 

Thanks to you both. Now I used the button states and deactivated "Restore on mouse". And I deleted all dozens of triggers and started with just a few triggers.

My only problem is that a selected button still hovers. Though I created a Rule like "Change state of Button Suche to Hover When the user hovers over the Button Suche BUT only when state of Button Suche is not equal to selected".

See attached file. 

Any idea?

You have too many triggers, there is no need for triggers to change to selected or back to normal if you use a button set. All the built in states work without the need for triggers.

Although I don't think you need a button set or selected state, may be better to use disabled state here. See the file I have attached.

Awesome. That works. Thank you. But........

What did I wrong? My trigger should logically be correct, isn´t?

Hover is an automatic state so it will hover without a trigger you cannot stop it only block the mouse, your trigger will be firing but is unnecessary and hence your condition cannot work.

Great explanation, thanks. And why does the "Disabled" state work instead of the "selected" state? Isn´t that a bug?

Selected state is intended to have a hover state. As you don't want one the disabled state does not have any active listeners such as hover enabled and is a bit closer to how a web page works

The "visited" state also worked for me.