I think Shi is just probing Yuzumori and thus provoked her that way intentionnally to see how she'd react, probably trying to figure out just how much do that little girl care for that new friend she made.
Probs cus Yuzumori's first comment was ambiguously passive aggressive and Shi-chan was like "??? Did she just...?"
I don't think Shi-chan planned on really saying anything to her at all, just maybe observing and figuring out what kind of kid Mimika seems so taken by, but Yuzumori's comment alerted her, and out of curiosity and/or fun, decided that it was a good chance to poke at her a bit to figure that/her out
If Yuzumori was just "good for you" with no trace of annoyance or jealousy at this obvious taunt, it could mean that she has some ulterior motive to let Mimika hang around her.
It's only a taunt if Shi-chan's closeness to Mimika actually bothered Yuzumori, which Shi-chan wasn't sure about and wanted to find out.
I feel like, if it hadn't bothered Yuzumori (like, if she wasn't really jealous), she would've answered something like that too ("good for you"/"how nice" or something)
I feel like the main 3 ways she could've reacted was really:
Bothered: "Mhm, how nice" (faking it)
Bothered: Visibly annoyed (more direct confrontation)
Not bothered: "How nice." or "??? Ok?" (doesn't notice, or confused at Shi-chan's tone/tryhard bragging)
Btw, why is it considered that Shi-chan fucked up? I just don't think it really mattered, how it went, what Yuzumori thinks of her. I mean, it's not like she was trying to get on her good side, with those comments.