1. What does it mean?
When contrasted with 비계, 공계 often means 공개 계정, an account open to public viewing. In artist, brand, or organization discussions it can instead shorten 공식 계정, the officially operated account.
Also written or said as 공개 계정, gonggye
2. The nuance
Visibility and authenticity are different things. A public account is not necessarily official; check who runs it instead of treating the abbreviation as verification.
3. Examples
“이 사진은 누구나 볼 수 있는 공계에 올렸어.”
I posted this photo on a public account anyone can view.
“공연 시간 변경은 주최 측 공계에서 확인했어.”
I confirmed the concert time change on the organizer's official account.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.