Depending on the amount of mana I use with SoV I keep popping into and out of invisibility, albeit without any messaging. It appears to happen whenever I reach full attunement.

I enter invisibility every time the spell pulses:

<<You maintain control of the Steps of Vuan spell.
<<Strands of refractive light surround you, covering you and hiding you from view.

Using a third person PoV to compare to what is happening on my first person PoV, it appears that I show up in the room look without messaging (and can be looked at, interacted with, etc) whenever I reach full attunement after the previous pulse:

<<You feel fully attuned to the mana streams again.

Whenever I use enough mana in SoV to never regenerate to full between pulses then I never leave invisibility.