Being a concert pianist myself and having spent my whole life practicing piano I believe I might bring something to help you becoming a better sight-reader.
First of: sight-reading IS the ability to play a piece of music for the first time and make it sound as if you have played it your whole life. “Make it sound” does NOT mean without mistakes, it means (you) being able to capture right away the essence of what the music should sound like and then being able to transcribe it accurately to your audience. Sight-reading is NOT (and that’s a common mistake) about playing the (right) notes! ;) ... Sight-reading is about playing the souls of the music WITHOUT STOPPING! Think of it as you, playing in an orchestra or singing in a choir. Never in a lifetime the whole orchestra and/or choir would stop because you (or someone else) made a mistake! ;)
The second point is about “How” to sight-read like pros?
first of all, there is a large range of amazing best concert pianist in the world who sight-read pretty poorly (Horowitz was one of them), and lots of pianists who sight-read amazingly and who can not sustain the pressure of an entire concert nor convey emotions during a performance!
Sight-reading is just a simple process developed by a part of the brain.. nothing more… like a muscle… Train it everyday and you will become good at playing pretty much anything at first sight..
But don’t get fooled, being able to sight-read anything and everything will never guarantee you the ability to be a great performer... it’s just two different “muscles” working in your brain... One is purely analytical and cold hearted (sight-reading), the other one is your “soul,” the one you pour in your music and convey to your audience... and you have that ability or you don’t… Being a good or a bad sight reader will not change that at all!
In a few words? Just practice a lot! Lol!