(Hebrew words will be spelt with English lettering unless requested otherwise)
I think it’s important to see this as a covenant and not as a sacrifice. Furthermore not as a “nathan beriyth” but a “karath beriyth” because karath has the meaning to cut, whereas nathan beriyth covenants would not involve cut animals in two.
The context is the following.
“But he said, "O Lord G-d, how am I to know that I shall possess it?"”
Genesis 15:8 ESV
In other words, Abraham is saying how will you confirm that you will do this for me. (Personally I’m surprised that G-d didn’t get insulted and didn’t see this as lack of faith coming from the father of faith himself). So G-d said I’ll make a karath covenant. Or what He actually said was
“He said to him, "Bring me a heifer three years old, a female goat three years old, a ram three years old, a turtledove, and a young pigeon."”
Genesis 15:9 ESV
Basically G-d is saying I will swear on myself that if I don’t do what I said I will do, likewise should be done to me. That was the ancient practice of karath beriyth. You didn’t even need to say anything. You could have had two nations that didn’t speak each other’s language and if the two kings simply walked in between the split carcasses it was understood that they made a covenant (of peace). And it represented the idea that if te covenant is broken, the culprit would suffer the fate of the split carcasses.
There isn’t a lot of texts about these cutting covenants to indicate conclusively if a certain animal denoted a certain type of covenant. There are two recorded texts of extrabiblical origin one speaks of an ass/donkey being used and an oath was taken and another of a sheep and a covenant/curse was taken but that’s insufficient to my liking to conclude that the animal represented different covenant types. Though that may have been the case.
Also it’s not clear what happened with the birds, even if they were killed at all. Certainly they were not split.
I’m sorry I can’t speak to why these animals exactly were chosen but it wasn’t sacrificial it was covenant related. The fact that it was three split carcasses might indicate the solemnity of this act. One was sufficient, three must have inferred immutability, absolute certainty. And Abraham is not said to have walked between the carcasses. G-d was swearing or making an oath on Himself
“For when God made a promise to Abraham, since he had no one greater by whom to swear, he swore by himself,”
Hebrews 6:13 ESV
How did He "swear"? He "walked" between the carcasses.