I am personally finding the same issue with Japanese actually (not my daily driver, just tested out for situation confirmation). Also, the underline issue does not appear on the stock app for me either.
On the other hand, I see the underline even when searching for fonts in Bear settings.
Another finding: Bear works as intended when I first boot the app (no blue underline, [[ works as intended ). Then the problem starts as I start trying to input a Korean hashtag. From then on all Korean inputs starts to have blue underline.