True. I don't believe that Zoro is thinking "I'm gonna milk this Oden's Haki".
Oden's attacks dont have that aura because it was Oden himself using the sword.
Now we have someone else using it.
I don't know how much this "oden's aura/will" is actually having some kind of actual gain for Zoro's attacks. But Oda flashes Enma out A LOT. "I need to release Enma more", using Enma for that slash that cut the mountain horn, now Kaido recognizing Enma as Oden's sword, the Big Mom "that's no ordinary sword".
What I think is happening: Zoro is gonna get compared to Oden for some time. It MIGHT be only for this fight, or it might extend for a while.
The reason for that is, Zoro has currently 2 breakpoints regarding Oden.
1- Opening Kaido's scar. When he does it, that's when Oda will say "Zoro is now equal to Oden".
2- Turning Enma into a permanent black blade. That's when Oda will say "Zoro is now SUPERIOR to Oden".
So, until that second breakpoint is reached, Oden is still gonna me mentioned and used as a measurement for Zoro's growth.
It might be just until the end of this fight, or maybe it will carry over for another fight. That I don't have a very solid opinion on. But the rest seems to be they way we are heading.