Giving it back to you with presumably a big bill for new parts and labour, but without the starting problem fixed, seems very unprofessional of the garage.
Or is there anything else you haven't told us?
Did the garage say why they thought it necessary to install a new cam belt kit given the problem was not starting? That seems odd. It may well have been a good idea to do the belt if it was in the garage for other work, but only if they had first diagnosed and fixed the starting issue.
Was the car misfiring before it wouldn't start? Else why did the garage replace the ignition module?
Does the invoice give any detail as to the ignition module, crank and cam sensors that were installed and how much did they cost? Genuine GM cam and crank sensors are no longer available off the shelf. They're special order from Germany. At least a week to get or they've come from somewhere else.
The GM 4 pot engines have been available in various capacities going back years. They're all very similar, made in the millions and widely used in multiple Opel / Vauxhall vehicles and other marques. There's even a GM 2.2 in a Fiat, I seem to recall. So any garage who knows what a spanner is should be able to fix it.