Thank you for your answers.
There is no trace of liquid, especially behind the master cylinder. It would be really bad luck to have received a master cylinder defectful...but why not!.
I changed the fluid type with "blue racing fluid" which is very heat resistant and DOT4 compatible. What is amazing is that with a completely new system the dysfunction persists. I tested the booster, it works perfectly.
I’m gonna run a new purge and check my connection connections.