It’s not common but it’s not rare.
We had several over the course of three years in approx 1000 lambs born each year. ‘Anus’ became one of our standard newborn lamb checks. The vet told us it happened sometimes and didn’t seem to be hereditary, although we did cull mothers who had lambs with the condition and of course didn’t keep daughters for breeding.
It occurred in males and females. Sometimes you got the fissure into the vagina as you’ve described; those lambs could usually make it to slaughter weight. Sometimes everything was present except the hole, so the vet (or you if you were brave) could open it up. And sometimes - the majority in our few cases - there was nothing and the lamb would die or be Pts.
The ewes on that farm were predominantly Swaledales, with some NoE Mules (who were daughters of the Swales.). I can’t recall having the problem in other than pure Swaledale lambs, although we produced mainly Mule lambs. So there could be a breed factor there.
On the next farm it was commercial sheep, Texel and Charolais crosses, with Blackface ancestry and a few with Swaledale ancestry. In seven years there, with around 400 lambs per year, I only saw it twice. I don’t recall whether the mothers of those two had Swaledale ancestry.