gobject-introspection is hard to cross-compile but there has been some headway made by other distros:

• https://maxice8.github.io/8-cross-the-gir/
• https://archive.md/U8rm2

Older discussions:

• Always cross compile #21471 (comment)
• setup hook of gobject-introspection in nativeBuildInputs does not run with strictDeps #56943 (comment)