The sounds are a bit similar, but I can’t find any historical sources showing they could have a common origin…(old answer on this would indicate this is only coincidence ? Are nishi/higashi related to migi/hidari)
I would also say it is more of a coincidence.
Reminds me of a joke of 主人 and 囚人 being the ‘same’ as there is only a long vowel difference between them. Husband and prisoner respectively.