Yeah, I agree. I figured it could indicate what is considered to be the most “proper” speech. Dropping particles may be common, but it may not always be considered professional to do so, even in speech.
Like how in English schools, teachers will correct things that are commonly said but not considered “correct”. In my experience, I was told to stop saying “can’t” and say “cannot” a lot. Or things like
student: Can I go to the restroom?
teacher: I don’t know, can you?
So the context of her being a teacher + talking about good communication skills, I could see why the author may have wanted to highlight the missing particle in that situation. Not that it’s inappropriate (because, like you said, they are certainly not in a classroom setting haha), but that it’s funny given the context of who is saying what.
Edit in response to your edit! Yeah, using (?) instead of ◯ is weird. I can’t wrap my head around that. コミュ力 doesn’t seem like an unusual word, so I’m not sure why she would be doubting it.

Their little smiles after their back and forth were too adorable




Majime’s outfit was so cute, too!
