Hi,
I didn’t get any notification of dispatch after my passport was printed but I managed to track the delivery through the TNT delivery support page
https://delivery.tnt.com/tracking
First by entering postcode and application reference (PEX number). This shows the TNT reference number which you can use to track the delivery. Note that initially I was getting an ‘invalid’ message against the application reference which I assume meant that my passport had not been dispatched/picked up by TNT yet.