Apex Controller returns JSON serialized data for LWC and Aura : How to parse it

Flatten the returned data from your apex code

Data returned from Apex:

return [Select Name, profile.name From user where name like =: key];

Flatten the data so that you can easily access it.

//JS code in LWC or Aura
function flattenObject(ob) {
  let newObject = {}
  for (let i in ob) {
    if (typeof ob[i] === 'object' && ob[i] !== null) {
      retObj = flattenObject(ob[i]);
        for(let j in retObj) {
          newObject[i + '.' + j] = retObj[j];
        }
      } else {
        newObject[i] = ob[i];
      } 
   }
   return newObject;
}