ACKS has removed the "Identify" spell but it has replaced it with explicit mechanics to identify magic items in other ways.
p210 of ACKS: "Sages and other characters proficient in Magical Engineering or Loremastery can identify common or famous magical items simply through their knowledge of such things. Potions may be identified by sipping them, or by consulting an alchemist. Otherwise, an arcane spellcaster of 9th level or greater can identiy a magic item using Magic Research."
p117: "Spell research can identify a magic item. It takes 1,000gp and two weeks to identify a magic item, and a magic research throw is required. Note that potions and common magical items can be quickly identified with the Alchemy and Magical Engineering proficiencies.
The Detect Magic spell states:
If the aura emanates from a magic item, you can attempt to identify its properties (see Spellcraft).
Spellcraft states:
Identify the properties of a magic item using detect magic: DC 15 + Item's CL
So what, you might ask, is a "property?" Well, they don't define in a legalese way exactly what is included in a magic item's properties, except to note that it definitely gets you command words ("The spells detect magic, identify, and analyze dweomer all reveal command words if the properties of the item are successfully identified..."). One simply has to assume from general English definition and logic that it gives you anything beyond that, including what the item even does.
I think it's best to interpret "properties" as "All of what it does, including charges, command words, and whatnot. Its full rules stat block." (Excepting, of course, other defined exceptions like artifacts and spells on a scroll.) Analyze dweomer specifically says it gets charges, but relying on a 6th level spell to get the charge level of a plain old wand is pretty lame IMO.
In earlier editions of D&D I was fine with not telling people charges and letting them find out when they ran out - it added a nice randomization factor - but in Pathfinder where the Christmas tree syndrome tends to dictate that it's players' God Given Right to liquidate all treasure for a union-decreed cost to buy other gear, not knowing charges and thus value would be an impediment.
Best Answer
Not in 5e, but they did in previous editions
5e's rules don't seem to make any general connections between magical items and schools of magic. An active spell clearly belongs to a particular school, as all spells do; but magic item descriptions don't reference schools of magic. Detect Magic tells you the magical school associated with some magical aura, "if any", so it's evident that a magical effect doesn't have to belong to a particular school.
It would often be reasonable to say that a magic item which produces a particular spell effect, such as a wand or scroll, bears the corresponding school of magic of the spell, but there is no rule that states this is the case.
However, in earlier editions of D&D such as 3.5e, magical items absolutely were associated with the schools of magic. As described in the 3.5e SRD, Detect Magic tells you what schools of magic an item corresponds to, and every description of a magical item includes a note on the strength and schools (many items belonging to more than one school!) of its magical aura. DMs who are apt to describe magical items with particular schools of magic may well be familiar with previous editions and extrapolating to 5th edition.
In any case, it is of course up to the DM if they want magical item auras in their game to indicate a particular school of magic or not. I would prefer to do so in my games, since it's a good way of suggesting the likely function of an item without being explicit about it, and gives the impression of consistent rules of magic. I would consequently also rule that mechanical interactions based on schools of magic could apply to magical items, such as in the linked example of the Robe of Eyes, and so Nondetection should protect against the magical senses of the robe. That's definitely my personal house ruling, though.