They dropping lores doesn't mean Zoro will learn about that lores, unless they shout Zoro's lores in the middle of the fight for him. It's different from Queen and Sanji. Their connection was established since the start of the raid by Queen himself, and at the first moment of meeting, Queen immediately recognized Sanji as "Judge's son". Same with Jinbei and WsW, Oda immediately established their connection to eachother at the very first moment they met. Nothing remotely short of that for King. It's been 2 chapters and King still hasn't made that connection.
It's also possible Oda goes a different route and Zoro is not even really informed of this, but the lore is given to us the readers.
It's also possible Zoro never ends up feeling strongly at all about his Wano roots through out this whole arc
![Kayneshrug :kayneshrug: :kayneshrug:](https://worstgen.alwaysdata.net/images/smilies/symbols/Kanyeshrug.png)