Throat swabs are my least favourite STI test, so you have my sympathy from the start.
Yes, gonorrhoea is evolving and many previous treatments are less effective than they were. If they're talking about a jab, should you test positive, you will be getting two antibiotics together which should work, but your local clinic will be the experts on what's working locally. I would have expected that test results would be available quicker than seven days, particularly as it's recommended that you wait seven days after the jab before resuming relevant sexual activity.
Being particularly heartless, I would say that clients either knew or should have known that there was a risk in OWO, but they were prepared to accept it. If they have caught anything then I would say that it's 'Oh dear, how sad, nevermind' time. They are much more likely to know already, of course, because it has noticeable symptoms in the penis - feeling like you're 'pissing broken glass' is the usual description - much more often than it does in the throat.
The agency is not particularly likely to advertise this by contacting everyone who's booked anyone affected in the past three months - it would be extremely damaging commercially - but it's good that someone's decided that everyone should be tested.
Is continuing to work, but not doing OWO an option?