I know it's a running gag that Anya is kind of a dumbass because she's literally 4 years old and while it is true that she views certain things with a naivety that only a child can have and that she's not very academically smart compared to her classmates, it's totally overlooked how intelligent she actually is.
At this age she's not only able to read and write, she's trying to keep up with children who are two years older and basically have been trained to go to an elite school since birth.
Anya is very clever when it comes to hiding her psychic abilities, she knows exactly what will draw suspicion upon herself and avoids saying it, especially in front of adults. An example for this is how she acts in order to save the kid that's drowning in the hospital pool, she know she can't just tell her dad that someone is drowning so she just runs away with an excuse that seems logical enough for a first grader and it works! Mr chronic anxiety and paranoia himself didn't suspect her. Damian only suspects her being able to read minds because she's less carful around her peers. All of this is clearly a trauma response because she is afraid of rejection and of abuse, both things that caused lots of suffering in her past.
But those aren't the only instances when she shows her intelligence: she escaped a probably heavily guarded research facility on her own, when the terrorists plan to explode the building her dad is about to enter she comes up with a plan to stop the bomb from going off, she keeps track of everything that's going on during the missions (like the cruise ship), she covers for her mum and dad and she distracts adults in order to be able to do the stuff she needs to do.
She manipulates people based on the information she's gathered from mind reading. She's a bit clumsy at hiding this because what she's saying always seems out of nowhere but her being a first grader covers that up. Examples: she uses Loid's thoughts to fill out the crossword puzzle in order to get adopted, she tells her mum how much she loves her and never wants to be apart from her in front of Fiona, she tells Yuri she wants to get better at school for her mum's sake, she provokes Damian into meeting his dad when he has doubts, the list goes on.
Tldr: Anya is actually really smart for a four year old.
Don’t forget that she learned really fast that Yor is a) ride or die for her family; and b) ready to throw down at a moment’s notice at all times. When Anya gets into a situation where she needs some muscle, she knows all she has to do is come up with some excuse that will snap her assassin mom into action. (Like stopping that one bad guy at the aquarium by grabbing his shirt and not letting go, all while screaming about being kidnapped. Yor sent that man through the ceiling, no questions asked.)
