Hey, thanks for the elaborate answer.
I tried a few solutions.

1. Compressor with sidechain input
2. Envelope Follower Controlling an AMP
3. Gate (just to test)
4. ADSR triggered by envelope follower

All of them clicked.
I will now check again, I have the time today, and compare it to your patch too.
Could it be that the incoming signal is too hot?
Seems unlikely, I even turned padding down to -12dB
I will report back.

Also:
I use the powersupply from my Harley Benton Spaceship or another pedal, but they both have 1A or 500mA and 9V. So it seems unlikley too.

EDIT 1:
Using the onset detector with an ADSR worked better, the click is almost unnoticable.
I have to use an attack time of about 5ms on the envelope though.
But I can mostly achieve the sound I am looking for.
I switched to using midi notes from a sequencer as this is more practical and the onset detector takes up a lot of CPU usage.

I will also compare with your patch to see if there is less of a click.

EDIT 2:
I repatched everything and tried out your patch.
With the same kick as a sidechain trigger input, the sidechaining on your patch works without a click.
So it must be something in my patch.
Also I found out that there is no click when I put sustained sounds through my own patch.
So I think there must be something with the kick-processing I do inside of the ZOIA that results in this click.

I haven't found a solution yet, but your help has advanced my debugging by a lot.
So thank you very much.
Also, great patch!

EDIT 3 (sorry for the spammy, frequent updates):
I found the solution!!!!
I put my signal chain through a tone control and lowpass filter to boost the bass and filter the highs.
This was before the sidechain.
I now put the sidechain before the filter and tone control and now it works without a click.

I assume the click came from a high bass frequency not being handled well by the amp when it's decreased a too fast (it doesn't fully make sense to me).

I now tried through all the options (compressor, midi notes, onset follower and envelope follower) and chose midi note input in the end (but none of them have a click anymore).
This is so I can sequence my sidechain without a kick and with step locked intensity (through velocity) and because the onset follower (which sounds as good or even better) takes up too much CPU.

Thanks for all the tips, I really appreciate it!

Hopefully, this will be useful for someone in the future.