"Free" is adjectival when it describes something, as when it cites her as a "free woman…" eg, not married or in earlier times, not a slave, or as having "free will"
The use here is wholly different, the point being the difference between "wriggle freely" and "wriggle into freedom."
To "wriggle freely" is loosely to wriggle within the constraints of one's bonds… that is, left or right, up or down, back or forth as far as the chains or handcuffs, ropes or whatever permit wriggling.
To "wriggle into freedom" is to wriggle out of one's bonds. How great is that contrast?
I don't think Richard's expanding "she wriggled free" into "she wriggled in such a way as to become free" expresses that.
Here, "free" equates to the state of "beauty", not to the quality of being "beautiful". There are huge similarities among "she has beauty…" and "she is a beauty" and "she is beautiful…" but are they equivalent?
In this particular phrase, "free" does not describe "she" - nor even "her". The point isn't whether "walk free" is expanded as "walk in a free manner", but what that "… free manner" means.
Who doubts that "walk in a free manner" means exactly the same as "walk freely"?
Who suggests "wriggle in a free manner" or "wriggle freely" or "wriggle free" are comparable to those walks or, truly, to each other?
Despite Macmillan… despite even Oxford… "free", here, doesn't look like an adjective or an adverb when used with "wriggle" in that sentence.
No, here, "free" is a state, corresponding not only to "loose" but also to "away" or to any direction.
Will her being a "loose" woman work semantically, even if the grammar fits. Could we even suggest she was a right or left, up or down person?