How would I write a diary entry for Julia based on Chapter 23 of The Shakespeare Stealer?

To write a diary entry for Julia's experiences, thoughts, feelings and reactions as narrated by Widge in Chapter 23, you will need to think about what you know of Julia as she is during that chapter and to think about the conventions of diary writing. For example, according to how Julia's eyes and words say differing things in Chapter 23 ("her eyes spoke of sorrow") and according to the diary convention of writing in first person about feelings and emotions, you might start an entry with: "I harbor no ill will toward Widge," following that with how she does feel or what she does experience.
The conventions of diary writing specify informal, first person entries that are reflexive, showing personal thoughts, feelings, reactions and emotions expressive of the writer's personality during key moments in life (GCSE English Prep). Each entry has a stated date, and often a time and place, at the top of the entry and is addressed to "Dear Diary," often concluding with the writer's signature. 
We know some things about Julia as she is in Chapter 23. For instance, we know that Julia makes "no complaint" against coaching Widge in his role, that she says she "was glad it was" Widge to whom she had to "surrender" the role and that she showed him a "cheerful acceptance." Yet Widge saw that her eyes "shone with tears" in her "unguarded moments" and that her "cheerful acceptance was itself a disguise."
We also know that Julia originally refused the invitation to accompany the players to Whitehall, since the invitation was on "condition that she dress as a girl," but that at the last moment she dashed out "clothed in her costume from Love's Labour's Lost, her skirts lifted so high [they] could see her ankles." She says that she changed her mind about coming dressed as a girl, choosing instead to come "along in order to meet the queen." She laughs when Widge challenges her reason with "You lie."
For Julia's diary entry, the date might be "Summer, 1601." Since she is so attached to the Globe, she might write her date designation as "Globe Theatre, Eventide. Summer, 1601." To determine a date for an entry, look at what the story tells and at what history states if the story narrative is imprecise.

We know that the Lord Chamberlain's company performed the Thomas Dekker satire Satiromastix, aimed at Ben Jonson, in 1601.
In the novel, the company performs Satiromastix just before leaving to go to Whitehall to perform Hamlet for Queen Elizabeth I (it is not historically certain that Hamlet was performed for Elizabeth I).
We know that, in the story, the company had performed "Richard III" [sic] (p. 156) for the Earl of Essex "a few months" before getting their call to Whitehall to perform Hamlet; Richard II is historically confirmed as having been performed for the Earl of Essex in February of 1601.
We know that Widge and the company had "a fortnight," or fourteen nights, to prepare for their command performance.
This puts Widge's performance as Ophelia in Hamlet sometime around mid-summer.
So a chapter 23 diary entry, a chapter during which Julia coaches Widge to play Ophelia, could be dated loosely as "Summer."

It's the bits of information narrated by Widge, helping us understand Julia, that you can use to determine Julia's thoughts, feelings, reactions and emotions. You can use this to reveal her personality as it is framed in the experiences of Chapter 23: you can record in a diary entry these key moments in Julia's life. Remember to stay within the conventions of diary writing, others of which are to use correct grammar and punctuation, to use varied sentence types to increase interest and to use time and sequence referencing words such as, then, during, before, after, originally, finally and following.
https://targetstudy.com/languages/english/diary-writing.html

https://www.bbc.co.uk/bitesize/guides/zjdfr82/revision/1