Is this a common leak due to a bad seal, or does it look like it’s not seated all the way? Never noticed it before, but had the transmission built 1,000 miles ago. Would the trans shop had messed with this? It’s not a massive leak but I can see where it’s spinning and throwing oil all around.

Your seal looks like it has a small tear in it.  The shop may or may not have messed with that.  If you didn't have any work done to the t-case than they most likely didn't touch it.  I had my t-case resealed when I had my transmission rebuilt.  That seal started leaking the next day, I took it back and they put in another new seal and cleaned the shaft with some emery cloth and that seemed to take care of it.  

Yeah I just did a tail shaft seal on a 2006 Dodge (not Thor)  it wasn't too bad to do. Just the factory seal the outer dust cover failed and came apart but the inner seal stayed. Little digging at it, I got it out. 

The piece you see is the dust seal part of the seal, the actual lip is further in, I got one for my 3500 maybe 8 years ago but never did it, came across the seal the other day

 

Got mine from Rockauto

 

Easy enough to change, me I'd park nose downhill  if possible as we've just had our yard asphalted and wouldn't want even a spot of oil on it 

pull the propshaft, the transfer case end is a slip joint, hook the seal out either with a screwdriver carefully between it and the case or if there is a lip tap it backwards and carefully refit the new one, Ideally using a piece of pipe or a socket to drive the new one in, I save all kinds of things just for driving seals, oh and if the new one doesn't have dried sealant or plastic on the outer edge where it would seal to the case just wipe a small amount around it before you fit the seal.

Thing is when you pull the shaft out just inspect it where the seal lip is running, you may well find a wear groove, it is a slip shaft, seals are cheap so reseal it first see if it stops

Just replace the seal.   The reason this area can leak so bad, there is a pump on the output shaft and the bushing just forward of this seal is positively lubricated from the pump. there shouldn't be much pressure on the seal but there is constantly flow near it.

 

But if you keep having issues, you may need to replace the tailshaft bushing.  As the bushing goes bad, the wobble in the yoke really works on and wears out the seal quickly.

 

GL

Hag

Most of that oil is sent to the shaft bearings and spray the chain with oil.