Alias for rm does not include file name with @$

I am trying to create an alias for the rm command in the /root/.bashrc file on a VirtualBox Redhat VM (running RHEL 9). I cannot get it to work properly. This is an excerpt of my .bashrc file:

alias rm='printf "rm: cannot remove %s: Permission denied\n" "$@" &&  w >> /tmp/logfile_20090204_001.log'

sudo() {
	if [[ "$1" == "rm" ]]; then
		for file in "${@:2}"; do
			printf "rm: cannot remove %s: Permission denied\n" "$file"
		done
		w >> /tmp/logfile_20190204_002.log
	else
		command sudo "$@"
	fi
}

I reload it with . /root/.bashrc. The result I get when using rm is

: cannot remove : Permission denied

(no file name). I have tried replacing printf with echo, switching the single and double quotes and modifying the bash_aliases file instead of the .bashrc file, and nothing seems to work. How can I get this alias to print my file name (with and without sudo)? Thank you in advance for your help!