indeed

C1 is high school level indeed and C2 is academics. this has been studied on native speakers:

me> I'm looking for studies which examine citizens language proficiency in their native tongue in the European language reference framework i.e. b2 C1 C2

Gemini> https://share.google/aimode/bImgIsAl5VfAcuoFl

has links to studies

also here is the "self assessment" on the CEFR home page:

Self-assessment grid - Table 2 (CEFR 3.3) : Common Reference levels - Common European Framework of Reference for Languages (CEFR) https://share.google/E6POb6UYC53cUkxXg