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I just do not understand why I cannot use that function in my library, even though it is defined / available in the Gtk library.

$ nm /home/user/.local/built/lib/libgtk-4.so.1 --defined-only | grep x11_surface_move
0000000000461cc0 t gdk_x11_surface_move

You are correct that the function is defined in libgtk-4.so.1, but you are mistaken in that it is available: t in nm output means it's a local function. Such functions can't be called from outside.

There are a few reasons why a function may get local linkage:

1. the function is declared static in the file where it is defined.
2. the function is global, but is hidden at compile (-fvisibility=hidden) or link time (using linker version script).

The fix depends on why the function is local. For 1) above, removing static qualifier will do. For 2), you may need to add __attribute__((visibility("default"))), or you may need to edit the linker version script.