Related: Does casting a spell from an item allow you to apply class abilities that are used when casting a spell?
Alchemical Savant reads:
You develop masterful command of magical chemicals, enhancing the healing and damage you create through them. Whenever you cast a spell using your alchemist’s supplies as the spellcasting focus, you gain a bonus to one roll of the spell. That roll must restore hit points or be a damage roll that deals acid, fire, necrotic, or poison damage, and the bonus equals your Intelligence modifier (minimum of +1).
Spell-Storing Item reads:
At 11th level, you learn how to store a spell in an object. Whenever you finish a long rest, you can touch one simple or martial weapon or one item that you can use as a spellcasting focus, and you store a spell in it, choosing a 1st- or 2nd-level spell from the artificer spell list that requires 1 action to cast (you needn’t have it prepared).
While holding the object, a creature can take an action to produce the spell’s effect from it, using your spellcasting ability modifier. If the spell requires concentration, the creature must concentrate. The spell stays in the object until it’s been used a number of times equal to twice your Intelligence modifier (minimum of twice) or until you use this feature again to store a spell in an object.
So does a cure wounds cast using the spell-storing feature, and using the alchemist’s supplies to store the spell, benefit from alchemical savant? I think to answer this question a few sub questions need to be answered:
Does producing the spell’s effect from the spell-storing item count as casting a spell? Because casting the spell is requisite for the alchemical savant feature to take effect.
Another requirement for benefiting from alchemical savant is that you cast the spell using your alchemist’s supplies as the spellcasting focus. In spell-storing item’s case, you would be casting the spell using your alchemist’s supplies as the ‘spellcasting focus used to store the spell’, according to the requirements set forth by the spell-storing item feature. However, does alchemical savant require that you cast the spell using your alchemist’s supplies as the ‘spellcasting focus used in place of material components’? because being cast from an item means that there are no material components.
Some magic items allow you to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn’t expend any spell slots, and requires no components, unless the item’s description says otherwise.