Do you use Microsoft IME feature to emulate Japanese or Korean keyboard?
If you do:
The way a bank mode works, is that it creates an isolated environment, like a bubble out of your windows machine for the top online safety, however on the other side there are likely no apps and windows features for the reason. The only thing I can recommend you in this case to add an app using a + icon in the bank mode and add an app which would emulate your keyboard as Japanese or Korean. I'm afraid you can't simply add the Microsoft IME, but a third party app you trust, which won't compromise your banking experience
I think that none of our browser developers are really familiar with Japanese input methods and how does it work, if I didn't answer your question, would you provide please more detail regarding this issue?