No, the real call isn't until the electoral college votes on December 14th. The media is calling states when their projections are confident enough (and possibly when the difference is above the automatic recount threshold).

IIUC, litigation cannot (Constitutionally) change when the electoral college votes, when those votes are counted, or when the Presidency transfers. Assuming all states appoint electors in accordance with the safe harbor provisions of the Electoral Count Act, the "real call" is December 14th. If that doesn't happen, then it's possible neither candidate will have 270+ votes and in that case the "real call" is an unusually counted vote in the house.

With the current projections, it would likely have to be three states that fail to send electors properly for Biden to have a chance of losing.

Him conceding or not doesn't change anything. At worst the secret service will drag him out of the residence at 12PM 1/20

Donald Trump was called the Republican nominee for months before the convention even though you could say that was the "media" making the call. In fact, he didn't become the nominee until the vote at the convention was certified.

But it is completely irrelevant. Biden will be the next president.

The typical term is "presumptive". Trump was the presumptive nominee until the RNC met. Biden is the presumptive victor, pending completion of vote counts and EC vote. But people just shorten it to the (foregone conclusion of) victor.