[ci] [python-package] check distributions with pydistcheck (#5838)

.ci/check_python_dists.sh

@@ -17,4 +17,35 @@ if { test "${TASK}" = "bdist" || test "${METHOD}" = "wheel"; }; then
     check-wheel-contents ${DIST_DIR}/*.whl || exit -1
 fi
 
+PY_MINOR_VER=$(python -c "import sys; print(sys.version_info.minor)")
+if [ $PY_MINOR_VER -gt 7 ]; then
+    echo "pydistcheck..."
+    pip install pydistcheck
+    if { test "${TASK}" = "cuda" || test "${METHOD}" = "wheel"; }; then
+        pydistcheck \
+            --inspect \
+            --ignore 'compiled-objects-have-debug-symbols,distro-too-large-compressed' \
+            --max-allowed-size-uncompressed '60M' \
+            --max-allowed-files 800 \
+            ${DIST_DIR}/* || exit -1
+    elif { test $(uname -m) = "aarch64"; }; then
+        pydistcheck \
+            --inspect \
+            --ignore 'compiled-objects-have-debug-symbols' \
+            --max-allowed-size-compressed '5M' \
+            --max-allowed-size-uncompressed '15M' \
+            --max-allowed-files 800 \
+            ${DIST_DIR}/* || exit -1
+    else
+        pydistcheck \
+            --inspect \
+            --max-allowed-size-compressed '5M' \
+            --max-allowed-size-uncompressed '15M' \
+            --max-allowed-files 800 \
+            ${DIST_DIR}/* || exit -1
+    fi
+else
+    echo "skipping pydistcheck (does not support Python 3.${PY_MINOR_VER})"
+fi
+
 echo "done checking Python package distributions"