You do not need MinGW or MSVC. I have emsdk 4.0.15 only to build SDL3 to Wasm. Open CMD on the C disk and copy these commands:
> git clone https://github.com/emscripten-core/emsdk.git
> cd emsdk
> emsdk install 4.0.15
> emsdk activate 4.0.15
Note. It is very important to add this path C:\emsdk\upstream\emscripten to Path:
Unzip a fresh SDL3 source folder:
Open the CMD here and copy these commands:
> emcmake cmake -S . -B dist -DCMAKE_INSTALL_PREFIX="C:/libs/SDL3-devel-3.4.2-wasm" -DCMAKE_BUILD_TYPE=MinSizeRel
> cmake --build dist -j8
> cmake --install dist
And, please, show what is the result.