I almost feel like we are playing different AVNs.
I enjoy the world-building that Ocean does including reveals, like easter eggs, that I get to find when I am immersed in SG.
If you are not a big fan of world building or the interpersonal nuances that Ocean gave us, I could see the book club as being less for you than it was for me.
So - here is some of what I saw during the book club meeting:
Noji did not want the MC to attend the book club meeting, but we don't know why (either before or after the get together).
When we arrive, various people greet us, including Amber (our therapist) who acts like she has never met us before.
It turns out, through a little digging, that Noji and Amer have known each other for more than half a year, and yet Noji treated Amber like a stranger (in front of the MC) when she met her as part of the MC's first therapy visit less than one week past -- which makes the MC rightfully wonder WHY...
The MC gets into an argument with Charlie, who seems to be a/the book club lead - and Charlie turns out to be Robin's mom.
The various MILFs there include some that quietly (or Anna - not so quietly) hit on the MC, who can decide to play them for information and influence or not.
We get to see Amber and her sister Claire get into it a bit (which I enjoyed - some sibling disagreement also happens in my family, so I thought this was a realistic touch).
We find out that Sasha seems to attract the romantic/intimate attention of older men, and several have been forced to leave the book club due to their interactions with Sasha.
Katie Zane shows up after missing the regular meetings for months - and she pays extra attention to the MC and Nami - which Noji does not like At All.
We also find out that Sasha's Aunt, Inessa Petrova, is present, but as her bodyguard - which begs the question, who/what has prompted Sasha's family to assign her a bodyguard for something as innocuous as a book club get together (and does Sasha have a bodyguard while in school, like her redheaded friend).
You already alluded to Sasha's unanticipated knowledge of what the MC is going through on that balcony, and that she has medicine to help.
So -- I saw the book club as a very rich part of the story revealing new mysteries, advancing the story with Amber, Noji, Robin, Sasha, Katie Zane, and several of the MILFs as well as hinting at other mysteries.
As you said - your only take away was the MC/Sasha interaction at the end - while I noted and enjoyed that scene for all the reasons above and more.
This is why I almost feel like we played different AVNs.
Cheers!!