EA288 1.6 TDI (CLHA) - Positive block test (CO₂), coolant loss, EGR cooler or head gasket?

Hi everyone,
I’m looking for some advice from people familiar with the EA288 1.6 TDI engine.
I have a 2014 Audi A3 8V 1.6 TDI 105 hp (CLHA) with around 200,000 km.
For about a month, I’ve had a very strange coolant loss.
The coolant level can stay perfectly stable for several days, then suddenly the expansion tank is almost empty overnight. For example, I check the level in the evening after driving, everything is normal, then the next morning (engine completely cold) the reservoir is almost empty.
I have never seen a significant puddle under the car. When I refill the coolant, I’ve sometimes noticed a few drops underneath for a few seconds, then it stops.
The engine otherwise runs perfectly:
Coolant temperature always stays at 90°C.
No loss of power.
No hard starting.
No white smoke.
No oil/coolant mixing.
No check engine light.
A local garage performed a block test (CO₂ test) and it came back positive, meaning combustion/exhaust gases are getting into the cooling system.
The mechanic told me that on this engine the cooling circuit is quite complex (EGR cooler, heat exchangers, etc.). He doesn’t want to tear the engine apart without being sure. Surprisingly, he told me that he doesn’t think a head gasket is the most likely cause on this engine, and that he suspects the EGR cooler more. He has contacted Audi for technical advice and is waiting for their response.
My questions are:
Has anyone experienced this on a CLHA / EA288 engine?
Can a cracked EGR cooler actually cause a positive CO₂ test?
Would you go to Audi for a factory diagnostic, or to an independent VAG specialist?
Is there any known diagnostic procedure before assuming it’s a head gasket?
Thanks in advance!