However, Hinduism and Buddhism have developed parallel and usually seperate from their Abrahamic sister Faiths. Their narrative evolved over thousands of years is quite different. Yet Buddhism emerged from Hinduism as did Christianity from Judaism and the Baha’i Faith from Islam. Societal laws and those for spiritual development have successfully been put into practice and evolved over centuries or even Millenia. So in that sense there are clear parallels.
The language of "covenants" is a product of the Hebrew peoples being situated in the context of empires, with their suzerain and his subordinate vassal kings. They would bind themselves to him through sacred covenants sworn before multiple mutual Gods with divinely sanctioned curses for infidelity and blessings for fidelity. This originated with the Hittite culture. This became a metaphoric model to describe the relationship between God and humanity at large, and God and Israel in a sharper focus, as his "chosen people".
The specific tone and lists of blessings and cursing changes in the Biblical tradition reflecting the tone of the surrounding empire at the time. The original Hittite model of covenant was full of blessings and hopeful promises, with few cursings for lapses. Later under the Assyrian empire, with the Deuteronomic tradition came down from northern Israel out of this direct exposure to their ruthlessness with their God Ashur, Yahweh's covenants from them now reflect the Assyrian style of brutality with heavy sanctions and few blessings. God becomes very fierce and vengeful.
This is a shift you see within the Pentateuch. In both cases, it is against the cultural backdrop of these ruling style empires that serves as how people related to God, and envisioned how that God would relate to them, like their suzerain and them as a vassal kingdom to their God.
Now, how does this fit in with the Dharmic religions? It really doesn't. They didn't evolve such a way of modeling their relationship to God as the great king and vassal kingdoms. That was not their language, or their metaphor for basing their societies in some form of theocratic system as it was for those Near East empire ruled systems with binding covenentants with vassal kings.
The important takeaway here, is to realize that "covenant" is not something literal from God. It is simply a language, which actually barely makes any sense outside of a Near Eastern based theocratic system. It doesn't even make a good metaphor in modern times, since we live in entirely different sorts of systems of government and rules of power.
I had always struggled with the concept of covenant or kingship as a way of looking at God. It's the superimposition of a metaphor that doesn't really resonate beyond a culture where it originally would have. It doesn't really translate meaning in a meaningful, spiritual way. And that would in fact be why. Unless you knew what it was to live in a vassal kingdom as part of your daily reality, such a metaphor is too abstracted from daily reality to convey meaning.
How about the Eternal Covenant of God that is so well established in the Abrahamic Faiths? Are there parallels in Buddhism and Hinduism?
To try to find any possible parallels, you have to first strip away "covenant" and its original cultural contexts away, and try to understand underneath that metaphoric language of suzerain and vassal king relationships. What was it really trying to impart about the relationship between the Divine and the human realities, something which might express itself in other metaphors, other than "covenant"?
To try to get behind "covenant" at an existential level, I would suggest it has to do, originally, beginning in the priestly or more mystically oriented tradition with the realization of the blessings of following a spiritual life, and the human consequences for taking the path of death and destruction, selfishness and greed, and so forth. Those would in fact be basically the doctrine of Karma at its essence. Do good, reap the rewards from the Divine which is Goodness, Truth, and Beauty. Do bad and reap the consequences of "sin" or not following Goodness, Truth, and Beauty.
That's basically it in a nutshell, I would think just now off the top of my head. But I suspect there is quite a lot more basic human truth at the bottom of that convent metaphor.
BTW, as noted before once that priestly covenant metaphor got adopted by culture at large, then it becomes more influenced and representative of actual human social concerns, where violence and force is more prevalent. God's covenants then shift from "follow God and be blessed", to "Do it or else you'll be destroyed by God's anger!". That is a clear shift in tone, and a different application of the same metaphor.
Perhaps the traditions based on the Dharmic Faiths have diverged so far from Abrahamic Faiths the concept of an Eternal Covenant is rendered meaningless.
If you understand covenant to mean follow the Way of God, then you'd find that in Taoism, with the "Eternal Tao", or the Way. You'd find that in any basic religion that holds the the Ultimate Reality is Absolute Truth, Goodness, and Beauty, The Hindu term Satchitananda, "being, consciousness, bliss" echos that vision of the Divine Reality.
So all religions have somewhere at its core the recognition of the Absolute as Ultimate Goodness, or Perfection, and that to follow that as a pathway in life results in blessings and healthier and happier existence, free from suffering and illusions. That's the "covenant" right there. "Do this, receive the blessings. Don't do this, and reap the results of following the ways of the world." It's eternal, because this is the way of the Absolute. Everyone just uses different language to talk about it. The Hebrews chose "covenant". It made sense given their cultural backdrop. It was, and still is, a metaphor.