As you know, it is hard to translate a Korean word into English sometimes.
참 is a noun. it means "truth".
참으로 is an adverb. it means "with truth, really, truly"
참 is also used as a contraction from of "참으로"
너는 참 아름답다 literally means "you are beautiful with true words"/"My words are true, you are beautiful"
You don't need to mind the English meaning of "really" or "so".
참 means maybe somewhat between "really" and "so" in English.