I only care if it’s Chardonnay
The entire barrel regimen, yes, to some extent.
There’s a difference between “15 minutes in a big vat with a few wood chips” and “34 months in French oak barrels, 50% new”.
Yes, I’m very focused on the barrels. I do care about the cooperage because some just make the wine taste woody. Mostly, I’m looking for finesse and not bludgeoning any of the wines I drink with oak.