The contracting party is initially certainly the publisher, but the warranty naturally also transfers, so the end customer can report a defect as well
Your car example was good... If you buy new in Munich, you can of course still report a warranty claim in Rostock, you don't have to go to Munich
That would mean for the parquet that I could also turn to another company, which would then assert the claims for me. I consider that unlikely.
For cars, this applies as long as it is a contract workshop. If I go to a mechanic on the corner in Rostock, he cannot assert a warranty claim against BMW or will have a very hard time doing so.
The contact person here, in my opinion, is therefore the parquet installer. Of course, you can also inquire with the manufacturer and hope for goodwill. But it can also happen that the parquet installer then completely refuses to cooperate since his expert has certified flawless work. No one likes to be challenged like that, I know from my own experience...
And please always keep that in mind. The craftsman is also a human, not a robot.
The easiest thing will be, as always, simply to do the intensive care according to the manufacturer's recommendations yourself. The parquet layer will not do more than that...