Work around missing pybind in BYO LLVM build (#18916)

Installs pybind via pip to work around #18884.

Closes #18884.
diff --git a/build_tools/cmake/build_and_test_byo_llvm.sh b/build_tools/cmake/build_and_test_byo_llvm.sh
index 043bc98..d233664 100755
--- a/build_tools/cmake/build_and_test_byo_llvm.sh
+++ b/build_tools/cmake/build_and_test_byo_llvm.sh
@@ -24,6 +24,12 @@
 python3 -m venv "$VENV_DIR"
 source "$VENV_DIR/bin/activate"
 python -m pip install -r runtime/bindings/python/iree/runtime/build_requirements.txt
+python -m pip install -r third_party/llvm-project/mlir/python/requirements.txt
+# Note: IREE's Python bindings for Python 3.13 are build with support for
+# free-threading for which support was added to pybind with version 2.13.0.
+# Therefore, we upgrade to a more recent version and avoid mixing of different
+# pybind versions.
+python -m pip install pybind11==2.13.6
 
 # Note: by using the `build_llvm` action here, we are exercising byo_llvm.sh's
 # ability to build LLVM... from our own third_party/llvm-project. That's not
diff --git a/build_tools/llvm/byo_llvm.sh b/build_tools/llvm/byo_llvm.sh
index 0f3d0fd..d88fb57 100755
--- a/build_tools/llvm/byo_llvm.sh
+++ b/build_tools/llvm/byo_llvm.sh
@@ -113,6 +113,9 @@
 
   cmake_options="-DLLVM_DIR='${main_install_dir}/lib/cmake/llvm'"
   cmake_options="${cmake_options} -DPython3_EXECUTABLE='$(which $python3_command)'"
+  # Note: Building the MLIR Python bindings requires the installation of
+  # dependencies as specified in `mlir/python/requirements.txt`, which among
+  # others include pybind11.
   cmake_options="${cmake_options} -DMLIR_ENABLE_BINDINGS_PYTHON=ON"
   cmake_options="${cmake_options} -DCMAKE_INSTALL_PREFIX=${mlir_install_dir}"
   cmake_options="${cmake_options} -C $TD/mlir_config.cmake"