I remember reading this short story at about the same time, that I read this other story I asked about recently.
Short Story. Every time a child is born, the oldest person in the world dies
So it is possible they were both in the same anthology, but maybe not. I often am partway through several books at the same time.
I read this pretty recently, after 2020. It was difficult to judge when it was likely written, though it was probably after 1955. I may have read it online.
The lady suspects some traumatic event has caused her to suffer both amnesia and agoraphobia. She stays backstage in a theatre. The players treat her well, they let her stay and bring her food and other necessities. She decorates the place where she sleeps with things labelled New York. She believes the theatre to be in New York.
I believe the name of the theatre manager begins with S. He gives her lots of advice and support. She gets on well with all the players. She does odd jobs for them such as repairing damaged costumes.
During one performance, she glances out at the audiences and sees many strange creatures, some with two heads. When she asks the theatre manager about this, he tells her it was a special performance for a group of people on their way to a costume party. They perform a lot of Shakespeare, but also plays based on SF novels. One play wad based on a Heinlein novel, I think Methuselah's Children.
They put on a special performance of Macbeth, performing it the way it would have been done in Shakespeare's day. This includes young men playing the women's roles. Out in the audience sits what the protagonist believes to be an actress dressed as Queen Elizabeth I and actors playing her courtiers. She mentions to the players that this is an anachronism. Elizabeth I died before Macbeth was ever performed, but they do not seem.troubled by this.
They are struggling without really enough actors to play at the parts in Macbeth. The protagonist performs one of the parts, the first time she has done so.
They exchange the Queen Elizabeth I in the audience for one of their actresses dressed up as her. The theatre managers explains that the theatre travels through time. They are competing in a time war, trying to correct damage done to their timeline by their opponents. The protagonist says she wants nothing to do with them if they go around doing damage to history, such as kidnapping Queen Elizabeth I in the middle of her reign.
The manager.explains that the woman they kidnapped was not the real Queen, it was one of their opponents who wanted to damage history. Once she understands this, the lady joins with them to help with their missions.