Revert "Consistent with the configuration in the packaged cmake" (#26767)

Reverts #26104

It seems like this fix although is correct and necessary, it needs some
patches in some other places (like release pipelines and onnxruntime
inference examples). We will try and address the actual issue the PR was
addressing in a subsequent release. I will re-open all the GH issues
that the fix PR closed out so that the actual issue is still tracked.

Will reopen:

#24003
#26186
#23642
#25279
#25242

Author: hariharans29

tools/ci_build/github/linux/copy_strip_binary.sh

@@ -18,6 +18,8 @@ EXIT_CODE=1
 uname -a
 cd "$BINARY_DIR"
 mv installed/usr/local $ARTIFACT_NAME
+mv $ARTIFACT_NAME/include/onnxruntime/* $ARTIFACT_NAME/include
+rmdir $ARTIFACT_NAME/include/onnxruntime
 # Do not ship onnx_test_runner
 rm -rf $ARTIFACT_NAME/bin
 echo "Copy debug symbols in a separate file and strip the original binary."
@@ -27,6 +29,9 @@ then
     strip -S $BINARY_DIR/$ARTIFACT_NAME/lib/$LIB_NAME
     # copy the CoreML EP header for macOS build (libs with .dylib ext)
     cp $SOURCE_DIR/include/onnxruntime/core/providers/coreml/coreml_provider_factory.h  $BINARY_DIR/$ARTIFACT_NAME/include
+else
+   # Linux
+   mv $ARTIFACT_NAME/lib64 $ARTIFACT_NAME/lib
 fi
 
 # copy the README, licence and TPN