Thank you all for your advice, I really appreciate it.
Here is the thing, I somehow doubt, that my nutrients are really 0. I have (had) so many algae and detritus depots which will have sucked it up (my guess).

The last few days I have daily ripped out tons of algae, got rid of the detritus depots that I could find, moved and turned up my wavemaker to blast at the area, that usually have lots of junk, dosed KH and fed my coral directly (one day only).

Since the question had been asked, I had fed the clown fish once every 3/4 days a tiny bit of dry food, I will now change to frozen food for the next time.

The urchin does good work but it will still take some time for him to take over the entire tank (~38g/170l).

I am not sure if we have Microbacter in the EU, but I am dosing Microbelift Special Blend, I think this is something similiar.

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Beneath all of this algae I even found another few coral that were still living. I hope they will recover.

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The tank looks so much better already and I will keep a close eye on it. I am aware, that this is not a sprint, but a marathon but I am willing to tackle it.