Sorry, I am German native speaker and don't know much about the car technics in addition (I only can
drive cars

)
So what is the "VAQ unit"? You mean the mechanical diff on the front axle? Yes, the front diff of the TCR is not electronic (XDS) but mechanical.
But what means "open diff in the gearbox"?
Anyway, my gearbox is OEM hardwarewise but I have the software optimized (shifting times shortened, manual IS manual - no kick down, no automatic upshifting in "m" mode)
So you've not modified the gearbox ok thats fine....
Therefore you have a basic open type differential in the gearbox. The VAQ unit is not in the gearbox, but outside of it, & on your passenger side driveshaft. Its a modified Haldex AWD unit, & is basically an "electro-hydraulic multi-plate clutch system" to lock up the existing open differential, which is electronically controlled to shift torque between one drive wheel & the other, & it still uses the brakes to help the VAQ unit in certain situations.
Unfortunately, VW in their sales brochures wrongly call it a "mechanical diff"...which it is not......if it was it would be in the gearbox & replace the existing open diff. In car terms a "mechanical diff" usually refers to one in the gearbox in 2wd, & either a basic "open" type or a LSD (limited slip differential)
Borg Warner who are the manufacturers of the unit, call it “Front Cross Differential Technology”, or “FXD”.
ERWIN, which is the official VAG workshop manuals, call it a “Front Differential Lock”, & in the “Self-study guides” they also refer to it as an “Electrohydraulic Front Differential Lock”.
Volkswagen Audi Group HQ in Germany, call it “Vorderachsquersperre” (VAQ), which translated from German to English means “Transversal Front Axle Locking”, or “Front Differential Lock” depending on the translation website used.