Heidegger is not saying there's no subject-object distinction, rather he's saying that distinction arises from deeper and more fundamental relationships, in the same sense as we arise from the eternal nocturnal sea each morning to an island of rational consciousness.

In dreaming sleep subject-object relationships begin to bleed into one another and dreams themselves flow out of even deeper causal zones, ultimately back to the ineffable itself -- Being/God/One.

That is what one of the realisations of surrealism and ultimately all mystical traditions i.e. The chanting of AUM corresponds to A - waking consciousness, U - dreaming sleep, M - dreamless sleep, and the silent sound in-between each chant refers to the unknowable source of all things -- the ineffable. The chanting is cyclical, it cycles round and around, like Heidegger's three ecstasies of time which take you outside yourself (ego/subject) - past refers to waking consciousness, now is dreaming sleep and future is dreamless sleep. Remember, Aletheia is the chthonic goddess of the underworld -- not a transcendent unknowable concept like the Christian "God".

One thing to keep in mind is there was no such thing as the Western ego/subject prior to Plato. No Linear time, no deductive logic, no homogeneous subject predicates, no Euclidean space etc. The culture prior to Plato was oral, they used poetic language with singing and dancing rituals to remember (like how little children dance and sing around to remember their ABCs) and ultimately they lived in a different state of consciousness where the gods were intertwined with material reality as a fact of nature -- phusis.

The signs of the phonetic alphabet, as Plato noted, externalise memory and make us forget our origin. What Plato missed though was that in retranslating those new signs from a script you bias more the left brain hemisphere (as opposed to right) and that puts you into a conceptual space not previously in existence prior to Plato. That is why the essence of things for Plato i.e. the Forms are divorced from the senses and direct experience.

With Fixed forms and an absolute subject/ego a new type of truth comes into existence - correspondence theory - with its one-to-one correspondence from intellect to object and its instrument language which can only ever get at the surface of things (subject-object) as opposed to "the poetic" which references deeper relationships.

https://www.youtube.com/watch?v=7-P00IDJpvg

There was simply no abstract internal world for the pre-Socratic Greeks and there was no such thing as the Jungian/Freudian ego either, no conscious/unconscious distinction and no aesthetic representation either.