I found the reference design sorry about the confusion. Please see design post 10 is what the OP followed

 

So I just received new opamps from Amazon 30 minutes ago, tested it and still the same ...
I also tried to put a decoupling cap but still.

But could the fact that I used 47Kohm instead of 56Kohm be the problem ??

Precision : Those are LM358P, what does the P mean ??

And yep, as @Wolframore said, I made the circuit of #10

 

Or one better;
use another LM358 configured as an unity gain follower to buffer the Vref

And as AG mentioned, try the exact same values of the app note first. Once that it is operating correctly, you may change it to your heart's delight, and see what is the effect of that change.

This is a VERY common mistake in this and other forums. Someone copies a circuit from somewhere, but decides to perform a component change because: "I did not have a 10k resistor, so I figured out that 100K would work the same".

 

That buffered Vref is really clever !!

Yep I'll try to replicate the same exact circuits with every value as on the schematic, but I first have to wait for my resistors to be delivered haha (which is really slow in France these days for a well-known reason)

 

Since the circuit produces an AC output then a Vref capacitor makes Vref a low impedance and an opamp would also make it a low impedance.

That is your problem. Amazon sells underwear and shoes. They know nothing about if electronic parts are real or if they are fake.
What does P mean?? The datasheet and a real electronic parts distributor like Digikey says and shows what it means.

For the 50k or 51k resistors, use two 100k in parallel.

 

Well, I finally got it working with right valued resistors as You said !!

I have now learn from my errors haha and will first make circuits as I find them !

I wanna thank all of You for your help and sharing your knowledge, I have learned a lot thanks to you all !!

Thanks !!