I did have the same problem, and I think I found a way to work with the Bug meanwhile people of Squarespace fix it.
When typing japanese text, instead of do it directly in the webpage text box, you have to use the "Paste as plain text".
I'll upload a screenshot in which I typed the exact same phrase, one in the Plain Text Box and one on the squarespace box right in the editor.
I know the text box should work properly and hope Squarespace Team can fix it as soon as possible.
Hope this work for you guys. Or if anyone has a solution for this bug, we'll appreciate if you share it.