Yes, your sentence is correct:
"Equally significant, however, is the artistic legacy he left behind in Georgia, much of which was entrusted to the State Museum as part of his bequest."
This sentence is grammatically sound and well-constructed. It uses "equally significant, however" effectively to transition to the topic of the artist's legacy, and "entrusted to the State Museum" correctly conveys the idea of transferring responsibility for the artwork to this institution. Additionally, "as part of his bequest" clearly indicates that this was done according to his wishes or will.
Well done!