] Henry says he has a sister - but we're not given her name and she isn't in town yet.

Yes we are...at the assembly rooms in chapter 8. The ladies are even introduced to one another there.

"He looked as handsome and as lively as ever, and was talking with interest to a fashionable and pleasing-looking young woman, who leant on his arm, and whom Catherine immediately guessed to be his sister"

And...our Catherine is quite taken with Miss Tilney from their very introduction, so the threat to her friendship with Isabella is decidedly present from the first moment.

"Miss Tilney had a good figure, a pretty face, and a very agreeable countenance; and her air, though it had not all the decided pretension, the resolute stylishness of Miss Thorpe's, had more real elegance. Her manners showed good sense and good breeding; they were neither shy nor affectedly open; and she seemed capable of being young, attractive, and at a ball without wanting to fix the attention of every man near her, and without exaggerated feelings of ecstatic delight or inconceivable vexation on every little trifling occurrence. Catherine, interested at once by her appearance and her relationship to Mr. Tilney, was desirous of being acquainted with her, and readily talked therefore whenever she could think of anything to say, and had courage and leisure for saying it."