I find that 常識 is often translated as common sense, but to me the two have different nuances, even different meanings. In English, having common sense is more likely to mean "having the good sense to," say, look both ways when crossing the street. It has less to do with knowing something specific, like President Biden is a Democrat. The Japanese 常識 seems more expansive and encompasses both meanings; but perhaps with a greater emphasis on the latter, like knowing Shinkansen lines leave from both Tokyo and Ueno Stations. Am I right? And if so, is there a more specific term in Japanese for "having the good sense to"?
You are right, 常識 includes knowledge as well as judgement. Generally it means what the speaker thinks other people take for granted.
[補説]common senseの訳語として明治時代から普及。(emphasis added)
The following J-E dictionary entry has multiple senses :
A word for good sense and not knowledge is 良識. But at least to me, this generally refers to moral judgements. Assuming that is not always the case with good sense, it may not be a perfect fit.