Yoda to me feels very much like a spiritual guru who has stayed out of the way of galactic history for the most part, gradually growing in wisdom and power throughout his life. At some point Jedi began to seek him out for his wisdom, and they gave him the title of ‘Jedi Master’. His teachings are different than those of Obi-wan, leading me to believe that he adapted his long-form method of learning into a condensed Jedi training course, but this wouldn’t afford the same power as he has accrued through long centuries of meditation. This is why he is so astonished that Luke was almost able to lift the X-wing. He is concerned with Vader and the Emperor because of their dark influence, but he is not diametrically opposed to them. A force of nature as you say. He definitely identifies as a Jedi to some degree, hence his telling Luke that Luke will be the last only when he himself dies. Yet he tells him this in the context of ‘passing on’ what he has learned. In this way, a Jedi is one who knows about the light side of the Force and rejects the dark side. In this way most of all, Yoda is essentially a Jedi.