It's hard for me to tell if we are looking at tail protruding there, or if it's some sort of growth.
My last Dobe had a problem with his dock, and it was an open sore. The breeder said there was not enough skin to fix it while his ears were cropped. I was worried that it would get infected, especially because Oji had a major problem where he would pee and poop in his crate all the time – for months on end. His breeder told me that it would not result in an infection. That sounded amazing to me, but she is an experienced breeder and I trusted her. What could I do anyway? She turned out to be correct. No infection problem despite sitting and laying in poop!!
So Oji had a grey nub at the end of his tail his whole life. When he was young, it was sensitive and he'd yip a bit when it got hit, but eventually it was not. In fact, it only hurt me when I'd run into it – ha.
It is a short dock, yes; but it's not really uncommon. It's about the length that Oji's was. By the way, Oji's was docked using the old fashioned banding method. Do you know the method of her crop?
I don't want to stir the pot, but I have to wonder if you are experiencing the sort of discrimination that we run into as owners of docked & cropped breeds. Is the vet young? It's especially bad among young vets. Tail docking is not as triggering to today's vets as is ear cropping because several breeds, and some Doodles, still regularly get their tails docked. But it's just too easy for vets and their techs to take a dismissive or otherwise discriminatory tack with you when it comes to issues of cropping and docking.
Just keep a watch out for signs of infection, and take hope in what Oji's breeder said and how it came true.