What is the class of a spell cast from a staff?

Question

In D&D 5e when a character casts a spell from a staff (e.g. staff of a magi), what is the class of that spell? It is important for items like "+1 to DC for this class spells that you cast" from Tasha's.

Specific example:

• I am a lvl 20 Artificer.
• I am attuned to and holding a Staff of Power, and casting Hold Monster from it.
• I am also attuned and holding in my other hand (let's say DM would allow my hand to hold all of them, this is just for illustration) all of the following:
  • +3 All purpose tool (bonus to artificer spells I cast).
  • +2 Arcane Grimoire (bonus to wizard spells I cast).
  • +1 Bloodwell Vial (bonus to sorcerer spells I cast).

What bonus to DC will I get from these items when casting this Hold Monster?

Answer 1

The staffs details state:

While holding the staff, you can use an action to expend some of its Charges to cast one of the following Spells from it, using your spell save DC and Spellcasting ability

When you chose to cast a spell from the staff, you use your own spellcasting ability, whichever that is. You attuned as an Artificer, so you would use the artificers spell save DC and spellcasting ability, with the +3 bonus to Artificer spells. Some of these spells are not on the Artificers list of spells, but the artificer ignores "all class, race, spell, and level requirements on attuning to or using a magic item," so it is no problem for them to use any part of this item.
Say you are a wizard 10/sorcerer 10. When you cast the spell through the staff, you can choose to use your wizard spell save DC and spellcasting ability, or your sorcerer spell save DC and spellcasting ability, to take advantage of whatever you are attuned to.

Answer 2

A spell cast from a magic item is from no class.

A spell doesn't inherently have a class, since it can be found on the spell list for multiple classes (for example Cure Wounds is on the Artificier, Cleric and Druid list); when a Cleric prepares it, it counts as a Cleric spell, when an Artificier prepares it, it counts as an Artificier spell, and so on. A Cleric/Artificier multiclass can prepare it either as a Cleric or Artificier spell, depending on which number of spells prepared it counts against.

If the same Cleric/Artificier casts Cure Wounds from a magic item, it counts neither as a Cleric spell or an Artificier spell, since the spellcaster didn't prepare that instance of the spell and so didn't choose from which class it should be prepared from.

In conclusion, a spell cast from a magic item only gets bonuses that apply to any spell regardless of class; in your case, no bonus will be applied.