No "maiden" refers to her being female and the "man" part to her physical attributes (admittedly something missing from the series) but also her tendency towards traditionally masculine pursuits, feats of athleticism initially but later we see it extending to her desire to rule over lands and active opposition to Sauron.
You are kinda right about the toxicity though as Tolkien wrote the Noldor as pretty much the poster-children for toxic masculinity (except for Finrod the Best Elf) and Galadriel struggled with her share of that right up until she refused the One Ring at the end of the Third Age.