After the errata / Tasha’s, we know that you can use your character’s bonus action to command a Homunculus to use a Spell Storing Item. I think we also know that a Homunculus can freely maintain Concentration on a spell cast from the Item, as Concentration requires no action.
Let’s say the Item contains Heat Metal. The Heat Metal spell lets the caster take a bonus action on subsequent turns to re-inflict damage (and disadvantage) on the target.
Can the Homunculus take this bonus action without being commanded by the character?
The Homunculus description in Tasha’s states that
it can move and use its reaction on its own, but the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take another action. That action can be one in its stat block or some other action.
Note that nothing is said about its ability to take a bonus action, probably because the ability to take a bonus action is granted by specific circumstances (e.g., dual wielding light weapons), class features (e.g., Defensive Field), feats (e.g., Crossbow Expert), and spells (e.g., Heat Metal).
Absent anything more specific in the Homunculus description, one could argue that the specific language from Heat Metal lets the Homunculus take a bonus action at will. On the other hand, one could also argue that a "bonus action" is a subcategory of "action" — however, I don’t think such an argument holds water, because while some bonus actions replicate actions (like weapon attacks), others do not (like Defensive Field), suggesting that "bonus action" is a separate category of game mechanic.