Sounds like a general problem with ExternalProject_Add. How is cross compiling supposed to work in that setting?

seem the general way is
set(toolchainFile ${CMAKE_SOURCE_DIR}/cmake/toolchains/${toolchainTuple}.cmake)
.. then later

add CMAKE_ARGS -DCMAKE_TOOLCHAIN_FILE=${toolchainFile} in the ExternalProject_Add command.

I was able to get a verbose output that was showing me the before and after so I was able to replicate it with

set (EMSDK $ENV{EMSDK})
set (EMNODE $ENV{EMNODE}) # convert env to cmake vars for neatness

then inside the ExternalProject_Add on the CMAKE_ARGS set I have

-DCMAKE_TOOLCHAIN_FILE=${EMSDK}/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake
-DCMAKE_CROSSCOMPILING_EMULATOR={$EMNODE}
-DEMSCRIPTEN=ON

which then gets it building a emcscripten version of the sub project which then links fine.

IIUC -DEMSCRIPTEN=ON should not be needed since that is set within the toolchain file?

I didn't add it at first, but inside the sub project CMAKE file I had to make some changes under it being defined, and the code would fail to build with an error msg that showed my changes hadn't been made. I added the -DEMSCRIPTEN=ON and then the changes were put in and it built. I agree though that I don't think I should have needed too.