Sight reading is very common among vocalists. I personally am not a vocalist, but my first music education was not through the learning of a musical instrument. In grade 2 elementary school, kids in my school were introduced to the solfege system and sang before singing from the music staff where the scale can be moved from line to line for different voices. .....
This is my original world so I'll address it. I was introduced to this, and in grade 2. I became very good at it. In fact it was my only world for several decades. When I was given a keyboard and then a piano, I translated what I saw in the score into sound which I heard, and then played what I heard. I was puzzled, decades later and my first ever instrument lessons, when I brought a song to my piano that I loved, why he went to the piano to play "how it sounds" - since I heard it off the page. I have transitioned from that world. There are fallacies or weaknesses with it.
The first thing is that when you have Solfege, you go from the Tonic. So is the 5th note from the Tonic. Re is the 2nd note, etc. And you're assuming diatonic music build on the major or natural minor scale, with the harmonic minor and melodic minor as familiar derivatives. What happens if your music is no longer diatonic in that way? Get my point? Well actually it already fell a bit apart when I sang the Mozart Requiem, when it modulates - I wrote in interval names (I had a good ear for "M3" "m6" or whatever so I could do that.) - and Mozart is pretty diatonic and standard. I was good enough that the other amateurs with my voice cocked one ear toward me when they feared getting lost. It was NOT good enough for piano - not when you move out of the diatonic world.
You will learn to recognize intervals and triads so that at the end you can read and hear it in your head.
Melodically or harmonically? Back when I was still in that world, and my then-teacher tested what abilities I had, I could sing a major, minor, diminished or augmented chord; I could of course sing the intervals and "aug2" would simply have translated into "m3" so no problem. That was always melodically, one note at a time. In actuality, if I heard a fully diminished chord played harmonically (all notes at once), vs. augmented, I might mix up one for the other, or mix up dim for minor because I'd hear some of the m3's. Singing by its nature (unless you're a throat singer) is one note followed by another note. If you're in a choir you might get some ear for harmony - maybe.
Here's another problem. I look at the score, I hear the melody - I might even hear both the Alberti bass and melody in my head at the same time. It's in Db major. In order to pull it off, with those particular abilities, I need to have a solid sense of the layout of the piano keys - which ones are 'operational' for Db major so that I know my "Mi" is a white key, my "Re" is black. Otherwise I'll be in a "nope, not this one, go up a semitone" hunt. Been there, done that, discarded that t-shirt. Bought a better more versatile one.
Are you picturing the "melody in one hand", "chords in the other hand", diatonic music type of thing? What about music which is full of dense chords, polyrhythms, chords outside of keys, melody that goes along whole tone, octatonic etc? Are we supposed to hear these as singers?
Actually Ranjit started with different music than I did, and we have opposite strengths and weaknesses. He recognizes chords more than I do, relates them to piano keys more than I do - while I can hear melodies while looking at a score, and those things that come from being a singer and playing a passle of sonatinas when young since it's the only music I had. Said sonatinas were mostly diatonic. And yeah, I probably have some "talent". I'd not bank on that, though.
Topic: Intensity vs Duration of sight reading