I've never heard of a PET scan but it appears, from reading my link below, that I might have already had one (or, at least, a PET-CT scan anyway):
https://prostatecanceruk.org/prostate-information/prostate-tests/scans-to-see-if-your-cancer-has-spread
The answer to your question about it's purpose appears to be in this quote from that page: "The scan can detect very small areas of cancer". So the radiologist and cancer specialist will be trying to make sure that there aren't some areas of spread that weren't picked up by the previous scans.
I'm confused by the bit about having to remain very still after being injected with a radioactive dye though. In between receiving the dye and having my scan (which was only described to me as a CT one, rather than as PET or PET-CT), I hopped on a bus, went shopping and eat a pub lunch!