I'm so sorry to hear of your loss
I remember having our dog put to sleep, I just burst in to tears, sobbing, sniffing, snotting - the lot. The poor vet didn't know where to look or what to do tbh - I imagine its a difficult situation for them.
Remember vets train for a very long time and they may not have the best people skills at times but that doesn't mean they may not be an excellent vet.
Personally I'd rather a message be left I guess, because whenever I hear news like that I just totally break down (I wouldn't even be able to say good bye, I get that hysterical) so I don't have to worry about someone on the other end of the phone. Also I'd rather know when it happened, rather than some time after. But the problem is that every person is so different, vets can't please them all. Please don't think that because he left you a message he is a bad vetinary surgeon. Two totally different things, and as I say they train for an awful long time to be qualified, so I'm certain he did everything he could for your poor wee bun. So don't feel bad about which vet your bun went to, there is unfortunately, these risks whenever buns go the vets.
I agree that he should of tried the mobile before leaving a message though, seems a bit pointless taking a mob number and not trying it :? Perhaps speak to someone in the surgery or write a letter when you're feeling up to it, to urge them to try all numbers first. Feeling for you and bun