You remember this, but not the fact that she also has experience with blacking out?
Or is that what you mean by special connection?
I am actually surprised this plotline of Sara hasnt been picked up again for akiras current situation. Oh, wait, this is also optional conntent isnt it? *sigh* Now, after checking it doesnt look like it is. Well then it is even more of a mistake to not use it in some sort. I just hope this happens in the comming update, because if not i will really be disapointed. Because it just feels so weird when her bar is one of the few places we are cuttently able to visit for generic sandbox events and nothing with her has happened at all besides an event with rin that sort of felt pretty meh.
The Sakakibaras and Arakawas all blacking out and having mental issues is
part of what I meant by special connection. Sara has also appeared in Happy Events related to Ami and Sensei, and been implied to have been on the Untitled Children's Show, albeit basically all of this is missable if you're not fucking her.
The game even points out that nothing will ever make sense again if you miss Sara's recent events:
Nevertheless, after taking that stuff out, Sara still has been noted to have seen and talked to her dead son like Sensei does with Sekai, by Sana:
Overall: Sara and Sensei can likely understand each other mentally, better than most. They share quite a few similarities in their life.