Buddha means Discernment, and in deep meditation, we can understand the same as Buddha understood.

Buddha wasn't saying we do not have a soul, he was addressing that Self is an attachment to being a thing; when at a root level, we are part of infinite consciousness, which belongs to all selves.

The same when Buddha referred to the Source of reality, he didn't call it God or Brahman; Buddha used the terminology ‘Universal Mind’ in the Laṅkāvatāra Sūtra.

From Buddha's perspective, the soul is part of santāna, which means a continual evolving piece of music; where we all exist inside this Universal Symphony.

When we let go of attachment to everything (Nirvana), we realize we are all just part of the music; yet when we attach to things, this leads to suffering, as everything is transitory.

Buddha was trying to show how Dharmic ideas (Hinduism) with Self-Realization, had gone the wrong way; as Source is selfless, and the religion had become anthropomorphised.