To sync the Read status and the Read date there's an option in the settings inside CC where you tell the columns in Calibre where that information have to be synced, at least in the android app.
I'm translating from Spanish, but more or less this is the navigation: Settings -> Mark books as read-> and there are two options inside this menu(among others), one to tell the name of the column for the Read status, and another to set the name of the column for the Read date.
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