I've been watching a lot of Krzysztof Kieślowski movies lately, especially Decalogue, and I've noticed how adept he is at using visuals to externalise the inner ideas of his characters. How can I write screenplays that do that?
Part of that you need to leave to the director. Remember, that's the division of labor: you're telling the story with words, and he's telling it with pictures. And the actors are a big part there as well: that's almost the whole thing they're bringing to the table, that ability to figure out the character and then convey it with a nuance of expression and affect.
You can see writers like Tennessee Williams who try to convey the whole thing in the script notes, and he's certainly a great, but you look at all the performances, and you see they're not the same despite his exhaustive notes.
As a writer, the job is to make a good, fleshed out character. Someone with personality, motivation, and dreams. Someone a talented actor can run with, and a talented director can dream on.
If you're really good, they'll be doing it for a thousand years, in a thousand different ways.
It seems to me that you already have your answer: In the same way that Kieślowski does.
You will need to find visual symbols for mental states and processes. This can be color, light, weather, clothing, furniture and architecture, and the behaviour of the characters.
But you need to be aware of two things:
(1) While you might think that Kieślowski has managed to express the internal thoughts and emotions of his characters well, it is in fact the viewer who interprets the images, and very likely no two viewers come to the exact same conclusion as to what the images mean. That is, Kieslowski did not truly manage to communicate an exact message through his images, but rather he provided a projection surface for the ideas of the viewers. The context of the narrative might suggest certain interpretations, but in and of itself each image in the films is open to a wide variety of interpretations.
(2) Commonly the mise en scene is not the task of the screenwriter but something that the director and cameraman prefer to do when they interpret the script during filming. Kieslowski wrote (or co-authored) the scripts of his films himself. If you aren't also your own director, writing all the meanings into the script might be unconventional and not what your eventual director wants you to do.