Expression for "Puts the world into her person and so gives me out."

Solution 1:

It's nowhere near so gorgeous nor eloquent as the original, but the closest to the sense that I can think of is "to take it upon oneself" to speak for everyone.

Solution 2:

As per the OP:

Here the phrase "puts the world into her person and so gives me out" means "claims to speak for everyone else, representing her own opinion as the world's, and so portrays me according to that opinion".

I quite like this turn of phrase, but is there an idiomatic expression that captures this meaning eloquently in modern English?

The OP's text describes a person with a god complex:

god complex: A person with a god complex may refuse to admit the possibility of their error or failure, even in the face of irrefutable evidence, intractable problems, or difficult or impossible tasks. The person is also highly dogmatic in their views, meaning the person speaks of their personal opinions as though they are unquestionably correct. Someone with a god complex may exhibit no regard for the conventions and demands of society, and may request special consideration or privileges.

god complex: A person is who is said to have a "God complex", does not believe he is god, but acts so arrogantly that he might as well believe he is is God or appointed to act by God.

Beatrice in Much Ado About Nothing has a god complex in that she "claims to speak for everyone else, representing her own opinion as the world's, and so portrays [everyone in the world] according to that opinion".

God complex may or may no be sufficiently eloquent to address the OP's question. If not, the term god complex suggests at least one obvious alternative:

high and mighty: thinking or acting as though one is more important than others. Synonyms: self-important, condescending, patronizing, pompous, disdainful, supercilious, superior, snobbish, snobby, haughty, conceited, above oneself.

Solution 3:

I feel that the phrase as writ is the best "idiomatic expression that captures this meaning eloquently in modern English." The idiom suggests a couple of implications which rely on the context of the play to drive the dramatic irony home, but Shakespeare's precise diction encapsulates the general sense of the irony within the idiom.

For context, see first how Beatrice "gives [Benedick] out":

Why, he is the prince's jester: a very dull fool; only his gift is in devising impossible slanders: none but libertines delight in him; and the commendation is not in his wit, but in his villany; for he both pleases men and angers them, and then they laugh at him and beat him. I am sure he is in the fleet: I would he had boarded me.

And then she goes on to describe his imagined response to hearing these impressions secondhand:

Do, do: he'll but break a comparison or two on me; which, peradventure not marked or not laughed at, strikes him into melancholy; and then there's a partridge wing saved, for the fool will eat no supper that night.

Later, in his monologue, Benedick employs the idiom to describe the mechanism of her error in appraising his Real Reputation™.

But that my Lady Beatrice should know me, and not know me! The prince's fool! Ha? It may be I go under that title because I am merry. Yea, but so I am apt to do myself wrong; I am not so reputed: it is the base, though bitter, disposition of Beatrice that puts the world into her person and so gives me out. Well, I'll be revenged as I may.

In doing so, he unintentionally fulfills Beatrice's conjecture about his response, and—with great dramatic irony—validates that his sulking rebuttal is true to his "reputation".

TL;DR Irreducibly good idiom.