I can sight read piano music, it’s just a matter of learning how to read four separate staves.
This is more a matter of a habit connected to the motor activity of the eyes as conditioned from reading two-stave piano music. Of Course, you have already read four-voice music in that format, so bear that in mind.
Your eyes need to literally scan a greater vertical distance: imagine you have backed away a bit from the piano rack so you can now ’see’ those four separate staves with the same eye-sweep of your piano score reading habit. That is as much for reconditioning your eye motor habit as well as taking any ‘psychologically daunting’ aura off of the task. (It really is pretty simple.)
Practice: Incremental building up.
Scan, read, and play the soprano and bass only. That will get you used to that different range of eye-scan to which you are not now yet accustomed.
Then switch up the same, reading say, soprano and tenor — that octave transposition is dead easy, but it can be a hiccup until that too becomes a reflexive reaction. Then, try other mixed stave pairs.
Then do the same with three staves, shuffling which you read.
The same works for getting accustomed to reading orchestral scores: push yourself to read the outer voices, or merely the top and bottom, and eventually you are also more directly able to take in the inner activity.
It threw me for about, maybe two weeks, after which it became reflex. (Since accompanying became a third of my professional bread and butter, that may have been a helpful additional incentive. One likes to keep a job one likes:-)
It is not that far a distance at all in thinking, but the greater ’scan’ motor habit of the eye, and that tenor octave business — you can get familiar with it fairly quickly, by breaking it down as above.