How integral is the synergetic aspect of buddhism?

By synergy if you mean that you cannot do it alone, and God has to be with you or the universe should approve of you or whatever, then the Supreme Buddha’s Dhamma is not synergetic. The formlessness of the God, Yehovah and Allah has resulted in banning idol worshipping and making statues or drawing pictures of the "unmanifested" being forbidden. There are these do’s and don’ts in other aspects too of these religions.

That said in Buddhism, one needs the assistance of fellow Dhamma-farers who are fully established in the path, and the Devas, (at least up until you yourself is fully established in the path as a stream entrant) if one is to succeed in this path.

If the continuance of the round of rebirths occurs due to Dependent Origination, the latter must cease for the round of rebirths to cease occurring. The way to make that happen is to follow the Noble Eight-fold Path. To fulfil that process, one needs to association of noble friends, hearing the Doctrine and keep company with righteous people. He would also need a rebirth conducive to fulfil the process of following the Noble Eightfold Path. Now, that is where merit plays its part.

A rebirth in worlds of the Brahmas and Devas becomes a very helpful asset to one who searches for the goal of Nibbana. Such rebirths are the results of merits. So we must understand the true worth of merit. Those who spend the time arguing "We do not need merit but only wholesome deeds" unfortunately may end up getting neither.

Whoever is in the Noble Eight Fold Path – the road less travelled, need the company of Noble Friends who would encourage you in this path. When Ven. Ananda told The Buddha that 50% of the path depends on the association of Noble Friends, The Buddha corrected him, saying that it is depended 100% in the association of Noble Friends.

Sadly in the present day and age there are many so-called-Buddhists that bear misguided and false views harming themselves and many around them. In Sri Lanka specially, there are many who carry false beliefs while taking refuge in auspicious times according to asterism, auspicious signs, horoscopes, planetary objects, and the twelve houses of astrology. None of these have anything to do with Buddha’s teachings.

We live in an unfortunate time where the Asura Forces are far greater and stronger. One would only make one’s refuge in the Triple Gem impure by believing in horoscopes, following auspicious times etc. etc... Tell me how many of us ‘Buddhists’ have made the Sutta & Vinaya Pitaka (the Doctrine) of the Buddha, their teacher? It’s only a handful. We may say that we seek the blessings of the Triple Gem to protect and guide us, but what we go behind and look up to are the politics, the horoscopes, the auspicious times, the Asuras that we call ‘Gods’, and other ‘a’dhammas. So to overcome these we need the assistance of Davas who are well established in this path. In this way, the Supreme Buddha’s Dhamma is synergetic.

Many Buddhists in the present day may believe that beings in the worlds of Devas cannot accumulate merits. This view is contrary to the discourses of the Buddha. In the Doctrine, there is a meditation called the 'Contemplation of Devas'. In it the Buddha spoke about The World of the Four, The World of the Thirty Three, Yama, Tusita, Nimmanarati, and Paramimmita Vasavarti. These are all Deva Worlds.

A disciple who has developed the powers of a Noble learner such as faith, virtue, learning, liberality and wisdom, has the qualities to receive a rebirth in those Deva Worlds. Such a disciple with the powers of a Noble learner could contemplate: "Devas too have noble qualities that I possess. After my death in this world, I can receive rebirth among the Devas". Thus the disciple with the powers of a Noble learner does the meditation called 'Contemplation of the Devas.'

If one cannot lead a life of virtue and Dhamma in the worlds of Devas, The Buddha would not have taught His disciples how to meditate on the 'Contemplation of the Devas'. Another thing we know is that when the Buddha preached 'The Motion of the Wheel of Truth' (Dhamma Cakka Pavattana Sutta) only one person in the world of human beings reached fruition of the path, while Devas in twenty two worlds of Devas reached fruition of the path.

In Samyukta Nikaya there are discourses called Devata Samyukta and Devaduta Samyukta. When these discourses were spoken by the Buddha, there were many beings from the world of Devas who reached the fruition of the Path. Sakkapanha Sutta in Digha Nikaya (collection of long discourses) shows that Sakra, the Lord of the Deva world of the Thirty Three had reached fruition of the Path.

The Buddha's teaching was originally pure & unique. The synergism occurred when Buddhism traveled from India to China, Tibet, etc. In India, Buddhism also synergised with Hinduism, until it disappeared.

When I use the word "unique"; I am referring to the Four Noble Truths and other supra-mundane teachings such as The Three Characteristics, Dependent Origination & Emptiness.

Of the Four Noble Truths ,the Buddha said: "These were things he had never before" and called them: "The special teachings of the Buddhas" (MN 56 ).

Then the Blessed One discoursed to him a graduated sermon, that is to say, he spoke on the subjects of liberality, virtue, the heavens, on the evil consequences, the vanity and the depravity of sensual pleasures, and on the advantages of renunciation.

When the Blessed One perceived that the mind of Upāli, the householder, was prepared, pliant, free from obstacles, elevated and lucid, then he revealed to him that exalted [special] doctrine of the Buddhas, viz. Suffering, its Cause, its Ceasing and the Path.

https://suttacentral.net/en/mn56

~~~

273. Of all the paths the Eightfold Path is the best; of all the truths the Four Noble Truths are the best; of all things passionlessness is the best: of men the Seeing One (the Buddha) is the best.

274. This is the only path; there is none other for the purification of insight. Tread this path, and you will bewilder Mara.

Dhammapada

~~~

And the Blessed One spoke, saying: "In whatsoever Dhamma and Discipline, Subhadda, there is not found the Noble Eightfold Path, neither is there found a true ascetic of the first, second, third, or fourth degree of saintliness....Devoid of true ascetics are the systems of other teachers.

Maha-parinibbana Sutta

~~~

"Thus you should train yourselves: 'We will listen when discourses that are words of the Tathagata — deep, deep in their meaning, transcendent, connected with emptiness — are being recited. We will lend ear, will set our hearts on knowing them, will regard these teachings as worth grasping & mastering.' That's how you should train yourselves." http://www.accesstoinsight.org/tipitaka/sn/sn20/sn20.007.than.html

Did the Buddha ever talk about this aspect of (what has ended up as) his teachings?

Historically, "the Buddha" lived in what's now northern India (e.g. Varanasi) in maybe the 4th century BCE.

Buddhism migrated into China starting in about 100 BCE, which is where it met with Taoism.

And, according to Wikipedia, Bon started in the 11th century.

So I'm not sure it makes sense to ask whether "the Buddha talked about" Buddhism merging with Taoism and Bon, given that this meeting occured centuries after his life.

So I'm answering that, in my opinion, the Buddha didn't talk about it. The idea of his talking about it would be anachronistic.

If you want to know what the Buddha did talk about, I suspect our best rcord of that is what's recorded in the Pali suttas (and the Vinaya), which are e.g. as published on accesstoinsight.org and on other sites including these.

The Buddha did talk about or reference religious beliefs and traditions that were contemporary to his time and place (maybe Vedism, Brahmanism, and so on); sometimes implying some commonality between Buddhism and other schools or non-Buddhists (e.g. IIRC he says somewhere that he agrees with what the wise agree with), but more often pointing out some difference or distinction.

The question (of what the Buddha talked about) is complicated by Buddhavacana recorded after his death.

If you want to ask about, for example, the influence of Taoism on Buddhism, then I think you ought to ask a slightly different question: e.g. ask about the influence on a specific school of buddhism (e.g. Chan Buddhism) ... and maybe don't ask what the Buddha said about it.

The Buddha clearly identified his dharma as something that both transcends and complements religion, including teachers, rules, lifestyles, and ethics. He specifically invites his hearers to remain associated with whatever religion they have inherited, and implies that the dharma is perfectly compatible with all of this. See, for example,

"…you may think: ‘the ascetic Gotama says this in order to get disciples.’ But you should not regard it like that. Let him who is your teacher remain your teacher. Or you may think: ‘He wants us to abandon our rules.’ Let your rules remain as they are. Or you may think: ‘He wants us to abandon our way of life.’ But you should not regard it like that. Let your way of life remain as it was. Or you may think: ‘He wants to establish us in the doing of things that according to our teaching was wrong, and are so considered among us.’ But you should not regard it like that. Let those things you consider wrong continue to be so considered. Or you may think: ‘He wants to draw us away from things that according to our teaching are good, and are so considered among us.’ But you should not regard it like that. Let whatever you consider right continue to be so considered. Nigrodha, I do not speak for any of these reasons." (Digha Nikaya, sutta 25, para. 23; iii 56)

Elsewhere he tells a disciple who has converted from Jainism to continue to support the Jains with alms, and he disparages ethics, rules, and mere mechanical observances as inferior matters. He even warns against dogmatism, pointing out that dharma is beyond linguistic and rational categories.