Can anyone kindly explain to me what Higuchi is referring to when he says "That's all she ...

"That’s all she wrote" is an American phrase used to express the sentiment that one’s plans have come to an abrupt halt, that something has ended and there is nothing else to be said or discussed about the matter.

Higuchi is stating his love for her as a fact rather than an actual confession. He doesn't want her response- just is giving her information (because he already knows how she'll respond). He doesn't want to speak about that "confession" any further.

Thank you very much :)