How can I create an inspector that lets me select another script's variable.

That is not what that inspector is doing. The inspector in that image is allowing you to select a function to call whenever the value of the slider changes.

You can't really make something generic for what you want to accomplish... Maybe with a ton of work and some complicated code (and probably the use of reflection), but the closest I can think of that is reasonable is to start with an abstract class like the following:

 public abstract class StatBehaviour : MonoBehaviour {
     public abstract int GetStat(string statName);
 }

And then in every behaviour that has stats, inherit from this class instead of MonoBehaviour and override this method. Example:

 public class Player : StatBehaviour {
     public int Health;
     // ... other stats and such
 
     public override int GetStat(string statName) {
         if (statName == "Health") return Health;
         return 0;
     }

     // ... other Player class stuff
 }

Your StatBar script could then have two fields: one for the StatBehaviour to watch and one for the name of the stat to look at.

Note: A good improvement to make to this simple system is to create a Stat enumeration so that you don't use hard-coded strings.