How do I get the bottom right corner of a GameObject?

Assuming you're working with 2D sprites, you can just use this logic:

 // Start from the center and add half the width (ending up on the right side)
 float xValue = targetObjectRenderer.bounds.center.x + targetObjectRenderer.bounds.extents.x;
 // Start from the center and subtract half the height (ending up at the bottom)
 float yValue = targetObjectRenderer.bounds.center.y - targetObjectRenderer.bounds.extents.y;
 
 Vector2 bottomRightPos = new Vector2(xValue, yValue);

targetObjectRenderer should of course be a reference to the desired object's Sprite Renderer component.