Can I list the published papers that I did intern work for even if I'm not an author
However, I went to a CV writing workshop and was advised that any papers I contributed to in any way should be listed.


That's bad advice for an academic CV.  You only list papers on which you are an author.  I haven't ever seen exceptions to this rule - if you list them it will at best be confusing, and at worst seen as fraudulent.

You can certainly list your job as research experience, and in any graduate application, you can and should explain in more detail what you did and how it contributed to published research.  You should also ask your supervisor or PI to write a letter of recommendation which explains your contributions and their importance, and how it shows your preparation for graduate study.