Macbook M1 2020 -Apple Care country and purchase country relation (M1 Air 2020)

Travelling japan now . Osaka BIC Camera 4PM time - Purchased a brand new M1 2020 1TBSSD 512GB, 1 y warranty for 100k yen which is $1,153NZD , 667USD, 612EUR. Super rare in Japan as it has a US keyboard and it's a super deal. Got home 5PM- turned on battery dead . 1% - " Service recommended " Sealed for 4 years rendered battery dead. **Option 1** - full refund ( had to hustle BIC as they difficult ) **Option 2**- apple 1 year warranty- wait for replacement (1-2 weeks wait - so accommodating etc will cost) ***Option 3*** - AppleCare+- 27,000 yen (180USD ,$320NZD) Does apple care bought in Japan work for NZ AUS warranty?( will be living between New Zealand and Australia)? I have till April 17th to buy Applecare if I decide to keep it . But can I buy apple care from the New Zealand website for a JAPAN purchased macbook M1 2020- since that's my residence area after travels end? Online reddit, stackexchange give so many variations- some say its all international warranty , some say its better to get AC+ from place of purchase (Japan) Please advise..I have less then 16 hours . I will be returning to NZ and AUS after my Asia travels done . I have till tomorrow march 20 9PM for refund.