Once you start operating outside of standard major/minor scales all bets are off key-signature-wise. Especially in microtonal music, you can "invent" your own key signature as is most convenient to express your ideas.
Another way of looking at it is the distinction between diatonic and chromatic semitones. Obviously 12-EDO* doesn't distinguish between them, but 31-EDO (and 19-EDO) does.
A diatonic semitone ("between tones") is between two note names in the standard major scale, represented by B-C and E-F, and also by implication between F♯-G, A-B♭, etc.
Generally, you don't notate for 31-edo. Recall that we don't really notate for 12-edo either, otherwise there would be no such thing as enharmonics.
Rather, as long as you intend to use it for tonal 5-limit music, you should mostly notate for meantone tuning, which can apply to both 12-edo and 31-edo. I.e., you notate in diatonic tonality, just as you're ...
There are various different conventions. One of the more common ones is to incorporate symbols for
(Images are screenshots from MuseScore)
Of course, to compose in any "style" (using the term loosely here), it's highly instructive to study the scores of existing pieces. ...
There are two alternative notations for 31-TET. One of them uses double sharps and double flats:
The other ...