Monika is rigid in her athleticism, you kind of have to be wielding a giant, two-handed sword - not to mention her self inflicted regiment. In my head canon, she's a eternal opponent in a spar, going up against her Caladbolg is a form of training and equipment to swordsmanship and her own requirement to constantly improve herself. So, this "Aesthetic Squad" would be familiar with Monika without a doubt, if not already considered apart of it - unwillingly, of course. She'd consider the label childish at best with her strict ideals.