What is the status of Otzar Beit Din wine/grape juice that has Kedushat Shviit in someone else’s home if one is unsure if they performed biur or not. Is there a certain amount of time one can wait from the biur date of erev Pesach that there is a hazaka that the products in their possession are no longer from before Pesach but are after Pesach?

Biur Shvi'it [announcing it ownerless] is an obligation on the owner of Shmita produce [like wine]. If however he fails to do so the wine is still kosher and drinkable despite the unfulfilled obligation.