For Loop Fires Once In While Loop

Uhm, this line:

 bool powerUpOnGO = true;

has to be inside your for loop before the while loop. Once you set the boolean to false it will stay false. So currently you won't enter the while loop ever again once powerUpOnGO is set to false.

Though I don't really see any point in iterating through the whole for loop anyways. The way it works now is once you have found a location for the first "levelTag" you are essentially done. However if you implement the change as I mentioned you would check every object but you essentially ignore all results you get since you will always run through the whole for loop. So your final position would always be from the last "levelTag"

Also note that your continue is pretty pointless. You are inside a while loop and you would just start a new iteration in that while loop. This happens anyways since there's no more code after that.

This line is also completely pointless. It literally does nothing:

 powerUpPosition = new Vector3(powerUpPosition.x, powerUpPosition.y, powerUpPosition.z);

It's conceptionally the same as

 powerUpPosition = powerUpPosition;

To me that looks like you have several flaws in your logic.

If you actually want to find a position that does not overlap with any of your "LevelTag" gameobject you would need to swap your loops around. You would pick a random position and check it against all other positions. If any is overlapping you can abort the for loop and calculate a new position until the for loop completes without any overlap.

NOTE: The approach I just described does work but the time complexity grows unpredictably as the number of gameobjects increases. Also since we have a confined space at some point there's simply no more room to fit another object in. At this point the algorithm would never finish and your game would be stuck in an infinite loop, hangs and need to be forced closed. It's just something you should keep in mind. I would generally recommend to not use a while loop in the first place but instead use another for loop with a max iteration count of for example 20. If after 20 attempts no position is found we just give up. What you want to do in that special case is up to you.

So you probably want something like this:

 Vector3 GetRandomPosition2()
 {
      levelTagGO = GameObject.FindGameObjectsWithTag("LevelTag");
 
     for (int n = 0; n < 20; n++)
     {
         Vector3 powerUpPosition = new Vector3(Random.Range(minX, maxX), Random.Range(minY, maxY), 0f);
         bool powerUpOnGO = true;
         for (int i = 0; i < levelTagGO.Length; i++)
         {
             if ((powerUpPosition - levelTagGO[i].transform.position).magnitude < 3)
             {
                 powerUpOnGO = false; // we have an overlap
                 break; // so just break out of the inner loop and let the outer loop go around again
             }
         }
         // If we reach that point and powerUpOnGO is still true there was no overlap
         // so we have a valid point
         if (powerUpOnGO)
             return powerUpPosition;
     }
 
     // if we get to this point it means we haven't found any free position after 20 tries
     // so currently we just return the latest position
     return powerUpPosition;
 }

If you usually should have enough space to place your power ups this should work just fine. However if you want to prevent the powerup spawning when you run out of space, you need a different method signature since currently you can't really tell the calling code that there's no space left. The way you have setup your method signature, it always has to return a Vector3 position, no matter what.