A loose gas cap is not going to set an EGR code so more than likely you have an issue with the EGR. I would remove it and inspect it and if it were me, I would just replace it.
Here is a guide that will with testing it if you would like to do this:
https://www.youtube.com/watch?v=DqUCbbKdWf4
Below is the info for the EGR from the manual. Let's run through this info and let us know if you have other questions. Thanks
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Friday, May 21st, 2021 AT 1:19 PM