chmod -R: cannot access ...: Permission denied when gnuchmod gives Read-only file system

My downstream report for rust-coreutils=0.8.0-0ubuntu3: https://bugs.launchpad.net/ubuntu/+source/rust-coreutils/+bug/2152057 . Also tested 055a66b78ef86e3e18b0b96675f1e64110c1eac0

At https://askubuntu.com/q/1566581/1004020 , with ReadonlyRoot enabled, I tried

# chmod -R ugo+rX /lib/python3/dist-packages/
chmod: cannot access '/lib/python3/dist-packages/Onboard/__pycache__/OnboardGtk.pypy311.pyc': Permission denied
# chmod -R ugo+rX /lib/python3/dist-packages/Onboard/__pycache__/OnboardGtk.pypy311.pyc
# # See there's no error

It's similar for other subdirectories. Whereas with GNU coreutils:

root@daniel-desktop3:/lib/python3/dist-packages# chmod -R ugo+rX /lib/python3/dist-packages/zstandard
chmod: cannot access '/lib/python3/dist-packages/zstandard/__pycache__/__init__.pypy311.pyc': Permission denied
root@daniel-desktop3:/lib/python3/dist-packages# gnuchmod -R ugo+rX /lib/python3/dist-packages/zstandard
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/py.typed': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/_cffi.cpython-314-x86_64-linux-gnu.so': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/backend_cffi.py': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__init__.py': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/backend_c.cpython-314-x86_64-linux-gnu.so': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__init__.pyi': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__pycache__': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__pycache__/backend_cffi.cpython-314.pyc': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__pycache__/__init__.cpython-314.pyc': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__pycache__/backend_cffi.pypy311.pyc': Read-only file system
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/__pycache__/__init__.pypy311.pyc': Read-only file system
root@daniel-desktop3:/lib/python3/dist-packages# gnuchmod -R ugo+rX /lib/python3/dist-packages/zstandard/py.typed
gnuchmod: changing permissions of '/lib/python3/dist-packages/zstandard/py.typed': Read-only file system

The error message should be "Read-only file system" not "Permission denied".

Start by reproducing recursive chmod with ReadonlyRoot enabled on the paths shown, then compare the Rust implementation's error handling with GNU chmod when the filesystem is read-only. Done means the command reports "Read-only file system" instead of "Permission denied" for the affected paths.