Are you sure that the new column is called "file_name"? It should be "file_path" if you used the code I gave. I'd advise you to create a reprex so that we can see exactly what's happening by following this guide.
A minimal reproducible example consists of the following items:
A minimal dataset, necessary to reproduce the issue
The minimal runnable code necessary to reproduce the issue, which can be run
on the given dataset, and including the necessary information on the used packages.
Let's quickly go over each one of these with examples: