[mtlmtlmtlmtl]

It cannot(at least not efficiently). There's 64 squares which could contain any one of 6 pieces or nothing. So you would need multiple u64s. In addition you need to store things like castling rights since they depend on previous moves.

Engines these days tend to use bitboards, which is just keeping multiple u64s each corresponding to a board with all the white/black knights, kings, pawns, etc. This is then manipulated using various bitwise operations.

Edit: It's also worth noting that compactness is not the most important thing for board representation. Stockfish for instance only stores one copy of the position per thread, so the effect of any overhead there is negligible. It's much more important that querying and mutating the board state is fast.