considering I grew up with do-re-mi-fa-sol-la-si I find the mnemonics impossible.
But also, I don't understand the point: why not just write "A-B-C-D" rather than strange half filled circles?
The answer is: I have no clue, I think we do not actually account for flat and sharp when doing solfege.
Or better put: "si" was changed to "ti" in UK to be able to read chromatic alterations without ambiguity. Most of the latin and slavic world ignored this, AFAICT.
But full discosure: I know very little about music, music theory or music history, I just have vague memories of reading about it.