Kawamatsu says and I quote, "The soul that resides inside a katana makes a samurai strong and enables him to destroy his enemies."
This means that the strength of the sword - basically the sword itself - strengthens the samurai. If that has implications about Haki, then it quite literally means that every samurai is using the haki of the previous owner of their sword.
Yeah, it reacts to it since it contains Oden's soul. Not Haki though.
The sword is strengthening Zoro's performance since it's a powerup and that's what it's supposed to do. The Haki still belongs to the user though.
As I said, I don't think this is literally about haki (it's clearly Zoro's haki what Enma is sucking), but I wouldn't rule out something like Oden's soul affecting Zoro's haki, strengthening it or whatever. "Haki" and "soul" don't seem to be totally unrelated, hence why a person can keep their haki even with their "heart" (their self) put in a different body (Law's personality surgery) and translations like "spirit" have been given for
haki, so it feels a bit blurry. We will see, I guess.
Zoro has always fought independently up to now i don't see why that would change now. Kawamatsu words probably referred more to strengthening the spirit of the user giving them more courage rather than obtaining skills or abilities by those swords directly
In this particular case, such metaphorical interpretation doesn't really fit, for me, the emphasis on souls living inside the swords since it felt like such souls should have some kind of real impact on the new wielder's performance.
Regarding Zoro fighting independently, both Sandai Kitetsu and Shusui had properties by themselves that significantly empowered Zoro's performance and they were explicitly addressed in animistic terms. Don't see why Enma should be different, Zoro has always been carried (to a certain degree, not trying to belittle him here) by what the special properties of his swords could achieve.