1. Regarding noticing being transformed into a chicken
If the spell has no visual effect like Dispel, Mental Spike. It's imperceptible. With Subtle Spell, It's totally imperceptible. It's from Xanathar's rules
The relevant Xanathar's section is:
Many spells create obvious effects: explosions of fire, walls of ice, teleportation, and the like. Other spells, such as charm person, display no visible, audible, or otherwise perceptible sign of their effects, and could easily go unnoticed by someone unaffected by them.
You will note that it does say nothing about being unnoticed by
someone affected by them.
It then describes the possibility for onlookers to notice a spell being cast, which is irrelevant to the question at hand.
If you're Subtle Polymorphing, noone will know it's you casting the spell, but it won't make the people who started to transform into a Chicken and through an exertion of willpower (it's a WIS saving throw...) maintained control over his body form would "just feel bothered", except by DM fiat.
2. Regarding the ability to recognize spells
Additionnaly, if we were to subscribe to the idea that spells without visual cues can't be noticed, then we'd need to rerun the whole thread to correct some of the past affirmations. For example, in post #186 the OP proposed Counterspell as a defense against Power Word Stun, which has no somatic or material components, and nothing in the spell description states that one needs to shout the verbal component... Given the range, a whisper would be indiscernible, and certainly not recognizable as a spell.
Since by Xanathar you need to take your reaction to identify a spell being cast, the selective counterspelling policy exhibited in a few demigod build would be a failure, since there is no way to recognize a spell being cast before it is cast even with visual cues present, so you'd have to Counterspell "blindly".
3. Regarding the possibility to stealthily dispel buff because they don't have visual cues
Finally, it's the player decision to decide whether a spell he casts has a visual cue. Subtly Dispelling a Contingency, as was tried a few hundred posts ago, would be easily discernible since one would be interested to know whether his own Contingency is active or not ; one would therefore cast it by specifying, according to Tasha's suggestion :
Regardless of what type of spell caster you're playing, you can customize the cosmetic effects of your character's spells. [...] . The possibilities for how you might cosmetically customize your character's spells are endless. However, such alterations can't change the effects of a spell. They also can't make one spell seem like another-you can't, for example, make a magic missile look like a fireball.
It is canonically proposed as an example that the Haste spell might limn the target in faint thunderbolts. So, Haste has a visual cue despite nothing in the spell description mentioning it (because, it's a game of shared imagination and people are supposed to describe things...)