Samkhya assigns buddhi a specific list of functions distinct from what mind, ego or the senses do, and the classical texts are precise about the division of labour, because the whole soteriology depends on buddhi being the tattva where the decisive recognition occurs. Where manas merely coordinates sense data into a single presented object and ahamkara claims that object for a self, buddhi is what actually decides: this is a snake, or this is a rope; this experience belongs to prakriti, or purusha was never actually its owner.
The Samkhyakarika lists eight dispositions of buddhi, virtue and vice, knowledge and ignorance, dispassion and attachment, and power and weakness, four of them sattvic and four tamasic, which between them determine whether a given buddhi tends toward bondage or toward liberation. Knowledge here means specifically the discriminative knowledge that purusha and prakriti are distinct, and it is this disposition, cultivated to completion, that ends the mistaken identification driving apparent bondage. Because buddhi is prakriti and not purusha, this whole drama of ignorance and insight takes place entirely on prakriti's side of the ledger; purusha, again, does nothing and is not actually altered by any of it.
Buddhi's priority in the evolutionary sequence, ahead of ahamkara and everything ahamkara produces, is therefore not incidental ordering. It reflects the system's claim that discernment is more fundamental than either the sense of self or the objects a self experiences, and that liberation is available in principle to buddhi in every embodied stream of experience, because buddhi is what every embodied stream of experience already has.