All of the wizard subclasses in the 2024 PHB have an feature called "[Spell School] Savant" which gives them two free spells in their spellbook from the school they chose to focus on, represented by their subclass. In addition, the features say
whenever you gain access to a new level of spell slots in this class, you can add one Wizard spell from the [Spell School] school to your spellbook for free.
At third level, when wizards gain this Savant feature, they gain access to 2nd level spell slots, a new level of spells. So I think a RAW interpretation of this feature is that wizards get to add three spells to their spellbook for free at third level.
However, since the feature already gives you two free spells at third level, I'm unsure if that's the correct interpretation of this feature. The feature already gives you two free spells at third level, and there's no clarifying text to say how the two parts of the feature interact.
Is my RAW interpretation, that wizards get three free spells (of the correct school) at third level, correct?