My limited knowledge on the North American colonial era is that the British had a rather hands-off approach to diplomacy with Native tribes. Treaties, declarations, and other such deals seemed to contribute to the separation of Native and British lands, straining their relationship instead of turning it into one of ruler and ruled. After the Treaty of Paris, the British showed little interest in maintaining a relationship with the Natives as well. Nevertheless, during the war for Revolution, those Tribes active in the frontier-lands seemed to actually help the British by attacking colonists in the west, and it would seem many tribes had ongoing agreements with the British.
What factors determined the ways in which the British carried out their imperialism in America vs the rest of the world? Why was the strategy with the natives to push them back into the frontier instead of subjugating them to rule like they did in much of the rest of their empire?
This is one of the questions that crosses a whole bunch of different disciplines and I'm confident those who study the history of Indigenous people and Britain's various colonies can provide more context. I wanted to add a bit of history regarding your first sentence.
I can't speak to the nature of diplomacy but can tell you they were very much hands on. In truth, one of the first documents related to education on what would become American soil was related to the education of Indigenous children.
The document is a letter from the Virginia Council in London to Sir Thomas Gates, the Governor of Virginia. Sent in 1636, it was an explicit order for the British colonists to seize Indigenous children and educate them in the manner of Christian British citizens.
You shall, with all propenseness and diligence, endeavor the conversion of a native to the knowledge and worship of the true God and their Redeemer, Christ Jesus, as the most pious and Noble end of this plantation which the better tools fact you must procure from them some convenient number of their children to be brought up in your language and manners. And if you find it convenient, we think it reasonable you first remove then from their priests by a surprise of them all and detain them prisoners, for they are all so wrapped up in the fog and misery of their iniquity, and so terrified with their continual tyranny, chained under with the bond of Death unto the Devil, that while the priests live among them to poison and infect their minds you shall never make any great progress into this glorious work, nor have any civil peace or concur with them. And in the case of necessity or conveniency, we pronounce it not cruelty nor breach of charity to deal more sharply with them and to proceed even to dash with these murderers of souls and sacrficers of gods’ images to the devil…
Source: Fraser, J. W. (2001). The school in the United States: A documentary history. McGraw Hill.
20 years later, the Virginia Colony established statues on the education of "Indian Children Held Hostage" and set up salaries for the men who taught said kidnapped children in the ways of British Christianity. Various advisory groups in Britain sent advice and guidance on education in Virginia and South Carolina until the war. While there are instances in Indigenous children and British children learning and playing together, particularly in the area that would become Martha's Vineyard, they happened because of individual decisions by individual British adults. With regards, though, to Indigenous children, Britain's goal was that of subjugation.