I dunno about other text to speech engines but android's reads "zhis" just fine because as far as I can tell, it's doing words at the phonetic/syllabic level. Same with "zhat zhing". sure, it pronounces it with slightly more of a Z, but at screader speeds it's not particularly distinguishable
espeak alternates between "z(t)h" and a chinese-sounding "zh", "z(t)hat shing" which is a an issue but still legible at speed
the default one in firefox on linux handles it pretty okay (using voice reader, at least)
Microsoft Zira pronounses them with sh sounds in a way that sounds sort of like a lisp
I can't test others right now but I think people are really underestimating screen readers even if you don't use the text replacement...
I'd love more tests and opinions here, but I don't know how much of an issue this actually is for screaders at this point, and how much is people extrapolating. They're better than they used to be.
if I had to use one that was bad at it, I'd use the text replacement though, since tagging won't actually help with that part.
(I have discovered another reader issue though: many start reading your profile every time someone clicks into a post you wrote. But tab skips it, ofc.)
