The Resulting Spell's School Still Applies
BUT - So does Wish's - there are two spells
Wish is a Conjuration spell; RAW states:
Conjuration spells involve the transportation of Objects and creatures from one location to another. Some spells summon creatures or Objects to the caster’s side, whereas others allow the caster to Teleport to another location. Some conjurations create Objects or effects out of nothing.
The only part of that description that could apply to Wish is the last bit: So basic use of the Conjuration Spell Wish "[creates] ... effects out of nothing" - namely: a spell - not just said spell's effect. From Wish's description:
The basic use of the spell is to duplicate any other spell of 8th level or lower. You don't need to meet any requirements in that spell, including costly components. The spell simply takes effect.
Not only does RAW specify that the spell (rather than just its effects) is duplicated, it also goes on to state that said spell takes effect - something it could not do if it were not first called into existence by the Conjuration spell Wish.
The character casts Wish, with all it's own attributes: Level, Casting Time, School, Components. Wish causes a second spell to manifest (it "simply takes effect") without the need to cast it, but with all it's other attributes. The only ones that are irrelevant are those that relate only to casting. One spell is cast who's effect is to conjure (rather than cast) a second spell, who's effects then manifest.
RAW states the Range/Area of Wish as "Self"; you don't cast Wish on another character, or an area or anything else like you may be able to cast another spell. The implication here is that while Wish is conjuring a spell, this secondary spell behaves as though cast by you (rather than by the metaphysical entity that is Wish). The only specified changes to this spell in RAW are it's requirements; nothing else is changed:
You don't need to meet any requirements in that spell, including costly components. The spell simply takes effect.
So in the case of Geas:
You cast Wish on yourself, which manifests the spell Geas as though cast by you, along with all it's attributes aside from requirements. Geas then affects the creature, and the spell effects you'd detect using Detect Magic subsequently would be those of Geas, including the school. You wouldn't detect Wish's presence on yourself, as it's duration is instantaneous:
Many spells are instantaneous. The spell harms, heals, creates, or alters a creature or an object in a way that can’t be dispelled, because its magic exists only for an instant.
Role play and flavour here are a fun side effect:
Roland (Ranger): Here - this is the perfect spot to make our final
stand against the horde. Gideon, could you do something to help us
out? Keep the Skeletons from getting too close while we pick them off?
Gideon (Cleric): Sure, if you give me the day and I gather the last of
my incense stash, I could cast Hallow which will...
Flora (Sorceror): *Mutters under her breath ... Done. Also fixed it
so you won't get all scaredy cat on us again Gideon.