You thinking this and it being true about the rules aren’t the same thing. Nothing about any of those skills work with identifying a spell, which are rules laid out in Xanathar’s.
In Xanathar’s, the rules clearly say people can perceive the casting of a spell only if it has a Verbal, Somatic, or Material component. If you remove all three, you don’t have a way of being identified as casting a spell.
As for what the spell is or does, the rules also cover this. In the same section, it states you must use a reaction to make an Arcana check (not Perception or Insight or Investigation) to identify what spell is being cast.
That’s the rules. And before you say “Xanathar’s is old and not 2024,” the 2024 PHB says this about perceiving a spell:
“Awareness of Being Targeted. Unless a spell has a perceptible effect, a creature doesn’t know it was targeted by the spell. An effect like lightning is obvious, but a more subtle effect, such as an attempt to read thoughts, goes unnoticed unless a spell’s description says otherwise.”
And the only mention of identifying a spell outside the identify spell is a sidebar in the PHB that says you have to take the study action to make an Arcana check to identify a “non-instantaneous” spell and nothing about instant spells. So the Xanathar’s rules are still the most comprehensive we have.
Just because you don’t agree with the rules doesn’t change them. Targets of spells don’t know they are targets until the spell is obvious or its description says otherwise.
I don't know what 5.5e says about combat, but 5e had this to say.
"In combat, most creatures stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you. However, under certain circumstances, the DM might allow you to stay hidden as you approach a creature that is distracted, allowing you to gain advantage on an attack roll before you are seen."
The relevance there is that in combat most creatures are alert for signs of danger all around.
"Most spells require the chanting of mystic words. The words themselves aren't the source of the spell's power; rather, the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion. Thus, a character who is gagged or in an area of silence, such as one created by the silence spell, can't cast a spell with a verbal component."
The relevance there is that chanting is not at all quiet, especially coupled with particular combinations of sound with specific pitch and resonance. You can't easily cast a spell with a verbal component quietly. The danger there is fairly obvious on a battlefield.
"Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures. If a spell requires a somatic component, the caster must have free use of at least one hand to perform these gestures."
Intricate gestures and forceful gesticulations would be a fairly recognizable source of danger on a battlefield.
The least obvious would be material components.
In my experience, DMs at the very LEAST use perception to allow folks to be aware of spells being cast in combat situations, and very often unless the battle is super chaotic or the caster is taking pains(making rolls) to avoid detection, DMs don't even require that much. They just say, this guy over here is casting a spell.
So while the rules don't explicitly say how to find someone casting a spell in combat, there are a bunch of other rules that when looked at, heavily imply that you either just know or at least get a perception check.
