I wonder how much of dyslexia transfers cross-linguistically
It turns out that quite a bit of it is dependent on the type of language; A person dyslexic in alphabetic languages is not necessarily dyslexic in logographic languages, because they engage different parts of the brain. For example, from this review of Chinese developmental dyslexia:
Converging behavioral evidence suggests that, while phonological and rapid automatized naming deficits are language universal, orthographic and morphological deficits are specific to the linguistic properties of Chinese. At the neural level, hypoactivation in the left superior temporal/​inferior frontal regions in dyslexic children across Chinese and alphabetic languages may indicate a shared phonological processing deficit, whereas hyperactivation in the right inferior occipital/​middle temporal regions and atypical activation in the left frontal areas in Chinese dyslexic children may indicate a language-specific compensatory strategy for impaired visual-spatial analysis and a morphological deficit in Chinese (developmental dyslexia), respectively.
It turns out that quite a bit of it is dependent on the type of language; A person dyslexic in alphabetic languages is not necessarily dyslexic in logographic languages, because they engage different parts of the brain. For example, from this review of Chinese developmental dyslexia: