Proof in what exact way you were afraid, confused or frightened. Did you fear bodily harm? What made you think that? Did the intruder move to attack you? Did they notice you?

The law is written such that you need to prove innocence, that is, the existence of these effects. If you cannot prove you felt this way you are guilty.

as any reasonable person in this situation would

That is not sufficient. It is always scary to be put into a situation where the need to self defence arises. You must prove your terror was exceptional.

According to law student material of a university:

The asthenic affect [confusion, fear fright] must be of such severity that the perpetrator is able to process the events only to a significantly reduced extent.

https://www.uni-potsdam.de/de/rechtskunde-online/rechtsgebiete/strafrecht/entschuldigungsgruende/notwehrexzess-33-stgb

Restriction of the Right of Self-Defense in Germany

The right of self-defense can be severely restricted in certain situations. Case law has defined several groups of cases in which the right of self-defense is restricted:

[…]

Excess in self-defense: One speaks of an excess of self-defense when the limits of self-defense are exceeded:

• “Intensive Excess of Self-Defense”: In the case of an intensive excess of self-defense, a disproportionately strong means of defense is used, although milder means would have sufficed.

Your link again. Do you read what you send?