dotars are taking about 5-8 days to process vehicle inspections at the moment , but that can change from day to day
submit a car day 1 , takes 5 days , submit another one next day takes 8 , next day who knows
remember it greatly depends on what is in the queue before you at the time you submit them . any problems with the paperwork and it will go back to the bottom to be reprocessed . on average cars get submitted 1.7 times so its pretty common for something to hold it up twice.
on top of that you have supplier issues , parts and services are not always available immediately
also good workshops are just plain busy and sorry but its usually 1st in 1st serve and you might have to wait your turn! if you were told 2-3 weeks then live with it , better a good job than a quick one