Unity editor scripting : how to execute two different actions with the same button?

The main problem here is that the editor instance is created when the object is clicked and the Inspector loaded. And then it is destroyed as soon as the object loses focus and the Inspector not shown for this object anymore.

=> Your flag toggleRigidBody is not persistent!

What you rather want to do is serialize the flag inside your object or even better: Serialize the reference itself.

This way you

• Have already access to the reference in your script in case you need it on runtime
• Have the reference in the editor for a) checking if it exists and b) being able to remove it directly

So having your class like

public class ContainerController : MonoBehaviour
{
    // Store the reference in a field
    [SerializeField] private Rigidbody _rigidbody;

    ...
}

The editor could look like

[CustomEditor(typeof(ContainerController))]
public class ContainerControllerEditor : Editor
{
    private SerializedProperty _rigidbody;

    ContainerController containerController;

    private void OnEnable()
    {
        _rigidbody = serializedObject.FindProperty("_rigidbody");
        containerController = (ContainerController)target;
    }

    public override void OnInspectorGUI()
    {
        DrawDefaultInspector();
        
        // Loads all current serialized values from the target into the serialized properties
        serializedObject.Update();

        // If the _rigidbody field is not assigned
        // try GetComponent as fallback
        if(!_rigidbody.objectReferenceValue) _rigidbody.objectReferenceValue = containerController.GetComponent<Rigidbody>();

        // simply put everything that belongs to one button click inside one if block
        // this is easier to maintain and read
        // Of course alternatively you could also simply have two completely different buttons to display 
        // depending on the value of "_rigidbody.objectReferenceValue"
        if(GUILayout.Button(_rigidbody.objectReferenceValue ? "Remove Rigidbody" : "Add Rigidbody")
        {
            // Is there a Rigidbody?
            if(_rigidbody.objectReferenceValue)
            {
                // Yes -> destroy it
                // There are two different destroy methods depending whether you are 
                // in Play mode or Edit mode
                if(Application.isPlaying)
                {
                    Destroy(_rigidbody.objectReferenceValue);
                }
                else
                {
                    DestroyImmediate(_rigidbody.objectReferenceValue);
                }
            }
            // Otherwise the field is currently not set and no component was found using GetComponent
            else
            {
                // Add the component via the ObjectFactory
                // this enabled undo/redo and marks the scene dirty etc
                // and assign it to the serialized property
                _rigidbody.objectReferenceValue = ObjectFactory.AddComponent<Rigidbody>(target.gameObject);
            }
        }

        // Writes back all modified properties to the target and takes care of Undo/Redo and marking dirty
        serializedObject.ApplyModifiedProperties ();
    }
}