With the current JSON response provided, the below snippet could work.
var jsonData = JSON.parse(responseBody);
console.log(jsonData[0].site);
pm.environment.set("site1", jsonData[0].site);
siteArray = [];
for (var i=0; i<jsonData.length; i++)
{
var site = jsonData[i].site;
//console.log(jsonData[i].site)
siteArray.push(`${site}`);
}
console.log(siteArray);