I shot some footage 3 years ago that I was going back through and really liked the PP I used for it. Is there any way to tell through the clip what the settings were for the picture profile? Any help is appreciated.

No, afraid not.

It's a good idea before you start shooting to dump the camera data (others menu) to the SxS card and then at the end of the day back up the entire card. That way you will keep a record of how the camera was set up and your picture profiles.