Kaido recognized it as Oden's sword.
That means it has to have something that is characteristic of Oden. Most people would go to say that it has Oden's haki as that is the most defining thing of a character in OP
Haki is literally willpower, and scabbards inherited that as they momentarily had Oden's ryou when they raided Kaido. Haki can also be imbued onto swords and left there - black blades are permanent CoA coating, so Shusui is constantly enveloped in Ryuma's own haki
If it is not Oden's haki, it still leaves out the question of what Kaido saw of it to figure out it was Oden's sword. Kaido is not a swordsman expert so very unlikely he admired Enma or even knew of its name to that extent, he only admired Oden the person himself
Enma can potentially have Oden's soul, as said by that fox
BM, user of the Soul DF, was also the first of the Yonko to realize there was something strange about Enma's aura giving more credence to Oden's soul being in Enma theory
Of course, there is always the possibility of Enma having remnants of Oden's haki despite not being a black blade, but more evidence is required for that to be convincing.
Whatever the case, Enma is no ordinary sword, and people who have fought Oden can recognize it as Oden's sword, so there is definitely something about Enma that makes it both Oden's sword and very powerful sword. You can take the two as mutually exclusive but rooftop narrative has intertwined those two traits so closely that you have to be biased to outright deny that possibility