Oneness of the Universe was the original thesis of the (Kuru-Pancala) Vedic Religion (Brahmanism, as opposed to the later religion, the multi-deity Hinduism) - centuries before Buddhism appeared on scene. But it was never fully understood and the actual practitioners were rather corrupted, showing all kinds of real-life behaviors that went contrary to their own ideal.
Buddha had effectively cleaned it up and re-interpreted from the perspective of his own experience-centric framework.
Basically, Buddha said, the All of our lives can be summarized to our sensory and mental experience. Since experience is All, having painful and conflicted experience is the essence of suffering while having peaceful and harmonious experience is the essence of happiness.
The highest happiness or bliss, is Nirvana, the complete cessation of all limits, divisions, and conflicts that would have induced suffering. This cessation of limits includes (among other things) complete and utter cessation of any and all I-making or self-identification. So once the individual mind stops identifying anything as "self", not even the universe, the true realization of that which the concept of oneness meant to represent is achieved.
Note how this is different from the Vedic experience of All Universe as Self. In Buddha's own words, that could be liked to a dog claiming freedom from the pole it was tied to, while still running around that pole a leash-length away.
In Buddhism the authenticity of the attainment is verified in practice as absence of any longing, grasping, attachment, identification, juxtaposing, and reification. Any kind of conflicted unsatisfied mind betrays still having some limits. The liberated mind has no limits, no position, no identity, no fixed form. It is beyond even the concept of oneness and off to the Unbounded - which is what the notion of oneness meant to mean anyway. This emphasis on direct experience and personal behavior that must be in line with the transcendental realization is the trademark of the Buddha's method.
The essence of this teaching was carried along the trade routes from the original birthplace of Buddhism to Kashmir and from there to China, where it grew into Ch'an Buddhism, and then to Japan where it got known as Zen. The essential practice of Zen is direct non-verbal transmission of the first-hand experience of this formlessness and limitlessness, beyond scripture and conceptual interpretation.
Part of Chan's inspiration for making the emphasis on harmony with the natural environment comes from the ancient Chinese tradition of Taoism which teaches a similar end-state but without tying it to the social, ethical, and psychological implications the way Buddha did.
Coming back to the original Buddha's teaching, the suttas often describe Buddhist path as progression of steps taking the student from confusion to the experience of oneness and beyond. For example in MN137:
"There is equanimity coming from multiplicity, dependent on multiplicity; and there is equanimity coming from singleness, dependent on singleness.
"And what is equanimity coming from multiplicity, dependent on multiplicity? There is equanimity with regard to forms, equanimity with regard to sounds...smells...tastes...tactile sensations [& ideas: this word appears in one of the recensions]. This is equanimity coming from multiplicity, dependent on multiplicity.
"And what is equanimity coming from singleness, dependent on singleness? There is equanimity dependent on the dimension of the infinitude of space, equanimity dependent on the dimension of the infinitude of consciousness... dependent on the dimension of nothingness... dependent on the dimension of neither perception nor non-perception. This is equanimity coming from singleness, dependent on singleness.
"By depending & relying on equanimity coming from singleness, dependent on singleness, abandon & transcend equanimity coming from multiplicity, dependent on multiplicity.
"By depending & relying on non-fashioning, abandon & transcend the equanimity coming from singleness, dependent on singleness. Such is its abandoning, such its transcending."
In other words, the Buddha repurposed naive oneness of Brahmins as a stepping stone to "emptiness" - the true state of shapelessness and limitlessness which is the end of suffering.
Just like the Buddhist social ethics of non-violence, truthfulness, non-intoxication etc. lead away from the objective causes of suffering, Buddhist practice of oneness (Brahmaviharas, Formless Jhanas) leads away from the subjective causes of suffering, and all this is culminated by the teaching and practice of transcending the limits of conceptual mind - Emptiness - which removes the very ground the suffering stood on.