I believe since Maharshi was a practitioner of hinduism for him "the self" (what they call Atman) was to be seen in all things, and the same everywhere.
So anything transient cannot be the self, hence is an illusion, or false.
He practiced Advaita vedanta. When exploring the non-duality of self vs world, there are fundamentally 2 approaches. Advaita Vedanta denies the existence of the world, only the (true) self is real. Buddhism denies the existence of the self.
A bit pedantic, and I could be wrong, but based on what I've read, my understanding is that Advaita (non-dualism) is not something you can practice, although there are practices in that school that can advance you on the path, like shravana, manana, nidhidyaasana.
It's more of a reasoning-, knowledge- and understanding-based system than anything else.
Jnana Yoga is the path.
Check out Swami Sarvapriyananda's talks on YouTube about Advaita.
I am not knowledgeable about Advaita Vedanta, I'm just repeating some simplified statements from Michael Taft's course on non-duality.
Enlightenment is profound, and unrelated to belief, or non-belief about the existence of the world. Mainstream Buddhism does not deny the existence of the world or individual persons, it states that our conception of the "self" is a mental construct.
From a subjective perspective, everything we experience is mind-constructed, and in that context, there is no difference between self and world; everything we experience is mind. This is the essence of buddhist non-duality.
I would further add that we do not know anything about the existence of the world, only that we perceive the world indirectly based on sensory input, and most of us conclude that the world actually exists. There is a movement in science that calls this fundamental belief into question, you can checkout writings and interviews with Donald Hoffman.
"Hoffman notes that the commonly held view that brain activity causes conscious experience has, so far, proved to be intractable in terms of scientific explanation"
That's just a fringe position. It may look good on Youtube or a TED Talk. But it has no scientific backing. It is certainly not a "movement" in science. They produced no evidence or even proposed any experiments. It's just idle speculation, not science.