as to the question whether the outgoing fast track behind A/B check in (on the left side of the check in hall) is exclusively for TG passengers or for all:
during Covid that was the only open fast track and was used by passengers of all airline
after second one reopened it was moved later to the far right of the check in hall.
Even when I check in at counters to the right at airlines other than TG, I was directed to the fast track to the right

so I also guess after both reopen, the one to the left will be TG exclusive and the one to the right for all other airlines