Dear kripa44,
Namaste!
Welcome to the forum.
About Bhagavan's teachings,well,in philosophical therms,His main teaching is certainly 'Nothing ever happened'. This is,sure,seen ans spoken from the perspective of the Self realized Sage. But,Bhagavan preached differently according to temperaments of many different seekers who came to Him searching for the Truth.
His ultimate teaching is certainly only Silence.
Yes,i could say He certainly preached Advaita Vedanta. But,i also saw aspects of all other philosophies and teachings in His words. So,for me,it is very hard to put Him in any category.
And there lies His Greatness actually. In every sense His teachings are much more than Advaita,Dvaita,and such. They are based on the Truth,and they incorporate all philosophies. The reason is everything about Bhagavan; His unique temperament,His beautiful nature,His way of approach to devotees,to all aound Him,to the world in general. And,most important,His way of approach to the Self. So to say. And there lies His liberality,how You call it. It is the same Truth,but the Truth preached from the mouth of one beautiful man,in every sense of this word. Of the One who spoke only from the highest state,from Love Itself.
So,'the Sage' is the right word to describe Bhgavan. Or how many call Him,the Silent Sage of Arunachala.
Advaita Vedanta or not, i find these classifications truly non important. And i could never make one. I feel,it would make everything about Bhagavan rigid and placed it in some category,when He is above all categories. Simply,the beauty would be lost.
In fact,that can be said for many Great Sages. They always preached the highest Truth,but gave it names only for our sake.
Regarding Sri Nisargadatta Maharaj,i find His teachings to be same as Bhagavan's. Leading to the same Self,same Truth and Reality. They only differ in temperament and style. Someone preferes Bhagavan,someone Maharaj,but again,it only depends on the temperament of each seeker.
With love and prayers,