[CI][C++] Update Emscripten to 5.0.3 #55416

Describe the enhancement requested

Update C++ Emscripten from 3.1.45 to 5.0.3 for the nightly job test-ubuntu-22.04-cpp-emscripten.
Python job test-conda-python-emscripten installs 3.1.58 because of Pyodide 0.27.1 and that will be updated separately by

• GH-47329: [Packaging][Python][C++] Build and test PyArrow against Pyodide 314 (2026_0 ABI) #47330

Component(s)

Continuous Integration, C++