Are you sure it is transmission oil? Not a leak or drip from above? Before you order parts and tear into it, or pay someone to do that, smell the oil from the leak. compare that to the smell of your transmission oil and engine oil. Transmission oil, especially used, typically has a distinct odor that you can tell apart from engine oil.
Based on your pictures, your car does not appear to have very many miles on it. It would be unusual for the output shaft seal to be leaking unless the stub axle has been removed in the past and a the removal or reassembly might have nicked the seal.
That's the right side axle seal which, as others have said, essentially never leaks. I'd look at other things that might be oozing down there and dripping onto the axle or transmission.
Unless somebody pinched the seal when putting the axle back in there's just no reason it would start leaking - the other end of the shaft is located by a bearing, so the only motion the seal has to deal with is rotation.
They're very long lived: My '92 Celica uses the same seal on its C56 transmission. I've had the shafts out twice and the original 1992 seals still don't leak a drop.