Update.
I have replaced the old shitty onesided intercooler with two-side 600x300 one, and placed the new BAM intake manifold.
It has made a slight difference in airflow at higher rpm range but CFs stayed at the same levels.
Please find the new logs attached
I get the idea of reducing the CR, but it seems to be worth the deal when trying to get over 370-380HP, not past 320HP.
I have seen some projects doing more than 360HP with 9.0:1 CR, so I am afraid that there is another problems.
What do you think?

Take it easy prj, I understand what you mean, thank you for your help with that.
Even though there are 9.0:1 pistons the head was skimmed two times and that may be the cause.
Can you recommend the proper head spacer to fit in

Best would be to change the pistons for proper 8.0:1 ones.

Alternatives:
https://www.bar-tek.com/de/1.8t-dicke-metall-zylinderkopfdichtung-bar-tek
Of course they don't say how much it drops CR. Height is quoted as 1.92mm.

https://www.turbozentrum.de/Dicke-Zylinderkopfdichtung-VAG-18T-Metallkopfdichtung
They say 0.5-1.0 and the price is very good. Height is quoted as 2.35mm.

https://www.034motorsport.com/head-gasket-compression-dropping-multi-layer-steel-20v-1-8t.html
Drops 0.5. Height not quoted.

Here's a website that uses a plate and they let you customize it:
https://www.turbo-concepts.de/motorenbau/audi-vw-seat-skoda/1.8t/rumpfmotor/verdichtungsreduzierung/149/verdichtungsreduzierplatte/spezial-kopfdichtung-1.8t-20v
And here is another one, that is cheaper:
https://www.lspeed-racing.de/product_info.php?info=p1603_audi-1-8t-20v-zylinderkopfdichtung-mit-verdichtungsreduzierung.html

I would just get the thickest one. The only thing the compression ratio is beneficial for on a turbocharged car on pump fuel is fuel economy, at least as long as it is higher than 7 or so.
So maybe you will lose 0.1L/100km, but you will easily and safer make more power. Which is the point I think?!

If your CR is now closer to 9.5 then the thickest variant will drop it around 8-8.2. I recommend using ARP studs with the proper torque too...
Alternative is the Turbozentrum multilayer, but the effect will not be that big. You probably need around 0.1-0.3mm extra thickness just to get back to your original CR. It depends how badly your head was warped when it was skimmed. And the Turbozentrum one gives you about 0.8mm over stock.

Keep in mind that whole timing map will need re-tuning on dyno, not just WOT. If you do not take advantage of the CR then the car will be slower off boost.

Also the 9.0:1 CR is ok for a standard K04, not for a turbo that can give 1.5x the output. The 9.0:1 is already a tradeoff between fuel efficiency and performance/reliability from factory.
You should be aiming below 8.5.
VAG dropped the CR by 0.5 going from 180hp to 225hp, which is only a 25% power increase.

He has TTE 480, not a K04...

Timing you have to find on dyno, my experience is that torque is always better when you get on the throttle, because with 9.0:1 CR knock limited absolutely everywhere at WOT, even if turbo is not spooled.

You can do tricks with spool, like using lambda 1 for quicker spooling as it creates higher EGT and so on.