adding my 2 cents as a linguist in training:

korean is actually spoken in a higher pitch than american english, but he finds it more comfortable to speak in what i will call "home korean", i.e. the lower pitched korean he uses with friends, than "public speaking korean". https://twitter.com/joonypear/status/1330782603876724736

when he speaks english, he switches to the pitch he's most comfortable using, which happens to work for the reasons i mentioned. korean also happens to not have a strong emphasis on intonation (variation in pitch when speaking), so when he speaks english he sounds a bit monotone.

now the controversial part:

what people mistake for joon speaking with an AAVE accent is him applying korean intonation patterns to english. one of AAVE's intonation markers is that declarative sentences (ex. hi, my name is RM) are spoken with low tones throughout.

go back to the clip. notice how, even though korean is typically spoken at a higher pitch than english but typically has no CHANGES in pitch, the way he speaks "public speaking korean" still has minor inflections in tone. THIS is what makes it uncomfortable for him.

korean doesn't necessarily need a strong intonation pattern because politeness is expressed through semantics, not intonation. the changes in tone, however, make his "public speaking korean" more expressive. when he speaks english, however, he goes back to his comfort zone-

by speaking with his "home korean" accent that lacks changes in tone. though he seems lively, his english seems to lack "bounce" for a lack of better words"; this "bounce" is the intonation pattern found in american english. he hasn't mastered it yet, so his english seems flat.

his usage of his "home korean" accent while speaking english is why some people accuse him of adopting an AAVE accent when it is not that. it's just him not having a complete grip on american english intonation and him slipping into a more comfortable accent.