I'd like to know why is Elsa so sad and unresponding in the last scenes. I can think of 2 possible motives.
Because she expected a date with Yvonne (look at her dressed up all pretty) but then Yvonne left and her hopes were crushed.
Or because she has realized that Yvonne is trying to hand her over to be cared for by another love interest; and it breaks her heart.
Which one is it?
Both. It's a low point. Elsa was ditched into a blind date by the person she loves, which must hurt. Elsa isn't oblivious to how Yvonne rejected her with a sense of finality by forcing her to go on a date with Garth, and Yvonne intends for the pair to date long-term. It shows that Yvonne doesn't plan to acknowledge Elsa's feelings, so Elsa may fall into her usual trap of feeling worthless.
Luckily Garth isn't blind to how the two are acting, and is a caring bro. Garth seems as caring as Yvonne but not limited to just one person, and he seems a bit uncoordinated, so I look forward to yuri strategy sessions and Yvonne getting jealous.
The book and play Yvonne loves were probably just thrown into the story for fun, but if Yvonne has a history of favoring books about quasi-romantic relationships between women then Garth would be a likely person to notice. Yvonne grew up with burdens of strict duties and compulsory heterosexuality, so in the off chance the story reveals how she suppressed herself, we'll probably learn about it from Garth before Ms Denial.