here's the requirements chart for June 1st on:
https://www.mofa.go.jp/ca/fna/page4e_001053.html
also:
Review on the requirement of the certificate of negative result of pre-departure test:
From 0:00 am (JST) on September 7, 2022, based on the New Border Measures (31), among all cross-border travelers and returnees from countries/regions where the B.1.1.529 Omicron variant becomes dominant, persons who possess a valid vaccination certificate of COVID-19 will be no longer required to submit the certificate of negative result of pre-departure COVID-19 test within 72 hours prior to departing from the original country/region. Please refer to 3. Quarantine measures (New) below for further information.