Is Charm Monster (or similar magic) obvious to bystanders that the spell is being cast?

I've looked at a number of sources, for example I've looked at the "Sage Advice Compendium" which reads:

Do you always know when you’re under the effect of a spell?

You’re aware that a spell is affecting you if it has a perceptible effect or if its text says you’re aware of it (see PH, 204, under “Targets”). Most spells are obvious. For example, fireball burns you, cure wounds heals you, and command forces you to suddenly do something you didn’t intend. Certain spells are more subtle, yet you become aware of the spell at a time specified in the spell’s description. Charm person and detect thoughts are examples of such spells."

Sage Advice Compendium, Page 11

This describes that the target is not aware if it has no perceptible effect; however in the PHB page 203, it reads:

Verbal (V) 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 o f silence, such as one created by the silence spell, can’t cast a spell with a verbal component.

Somatic (S)

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.

PHB 203, emphasis mine

This would say to me that a spell is quite obvious it is being cast by just about anyone (assuming you aren't casting it with subtle spell, as part of the sorcerers class features); however, in the PHB, it says this:

Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature's thoughts, typically goes unnoticed, unless the spell says otherwise.

PHB Page 204

So when we review these sources, it would say that the target is not aware, yet casting the spell is quite obvious if we look at what it says about the vocal and somatic components; furthermore, it says nothing about bystanders and if they would notice these charm spells.

So back to our original question...

Do bystanders or the target's allies recognise you are casting a spell?

I'm asking for a RAW answer please.