Is it necessary for the cook to be Muslim to ensure that the food is halal, and am I obligated to verify its halality, given that the host company in Japan has confirmed that they will provide halal food?

It is not a condition that the food preparer be Muslim. This is supported by the fact that the Prophet, peace be upon him, and his companions ate from Jews and polytheists. In Musnad Ahmad, it is narrated that the Prophet, peace be upon him, accepted an invitation from a Jew for barley bread and rancid fat. In the two Sahih collections, a Jewish woman brought him a poisoned sheep, and he ate from it. If the host in Japan undertakes to provide halal food for you, then there is no need to search further, especially since most of the food there is vegetarian, unless there is doubt about the presence of something forbidden. As for meat, you can ask them if it is ritually slaughtered. If they confirm that it was slaughtered by a Muslim or a person of the Book, then there is no harm. Abd al-Razzaq narrated from Ibn Mas'ud that he said: "You have descended upon a land where Muslims do not slaughter; they are only Nabataeans – or he said Nabataeans – and Persians. So if you buy meat, inquire. If it is the slaughter of a Jew or a Christian, then eat it, for their food is lawful for you." In al-Haytami's Fatawa, the report of a disbeliever or a transgressor about his own action, such as his slaughtering or purifying, is accepted. For example, a sheep slaughtered by a dhimmi was made lawful when he said: "I slaughtered it," and this is an expansion in returning to the principle of permissibility.