Gate 1: the dream
Crossing the bridge toward the goblin camp plays the artefact scene. On the next long rest, the Dream Guardian visits and Embrace Your Potential starts. That quest is what lets the party consume tadpoles for illithid powers.
Gate 2: the skill tree
Once Embrace Your Potential has started, consuming a parasite or recruiting Minthara opens the illithid skill tree.
Astarion, Gale, and Minthara are willing to use the powers. Karlach, Lae'zel, Shadowheart, Wyll, and Minsc need persuasion.
Halsin, Jaheira, and the twelve hirelings are not infected, so they have no illithid powers to use.
Gate 3: the body change
Partial-illithid comes later. It is a body change. On Honour Mode the save does not rewind it.
The powers page treats partial-illithid as a later body change, after the first powers are available.
Honour Mode turns save scumming off. The partial-illithid body change cannot be reloaded away on that single save.
Official site: baldursgate3.game.