Looks like you're having issues with Unicode fallback fonts on your computer. I'm not an expert on Mac Unicode fonts, but I have some experience, being last tortured in Unicode font hell re-implementing the 16-language shortcut tables for Lightroom Queen with my Any Shortcut plugin.
Experimenting with
ǧ on my LR 12.3 / Mac OS 13.4, it's always displayed regardless of which font is selected, albeit in a fallback font if the selected font doesn't contain that character. For example:
View attachment 21020
A google for "mac fallback fonts" shows this is a poorly documented, poorly understood issue at the Mac OS level, and there is nothing documenting how LR handles fallback fonts and whether it relies entirely on Mac OS or has its own mechanism layered on top. This article sketchily suggests that the default fallback fonts on Mac OS depend on the region and list of preferred languages configured for your system:
https://raphlinus.github.io/rust/skribo/text/2019/04/04/font-fallback.html
So to make progress on this issue, we'll have to play twenty questions, with precise answers required. This will let us reproduce the problem and identify a workaround:
1. In which exact page field in Book are you entering the character?