One thing I've noticed is how sensitive the forward- and rear-looking sensors can be. On my 2016.5 GT, if I've got the least little crud (ie, a stuck leaf, even a smaller one) over the sensing zone at the top of the windshield then it's a fair bet I might get some strange warnings and beeps I wasn't expecting. When things are mucked-up with crud in inclement weather, I notice my rear-facing proximity warnings (ie, for cross-traffic or a pedestrian) aren't as exacting, though no change in the warnings/beeps when it does warn. Of course, your 2016 <> 2023.
The key fob stays in my pocket. When my wife drives her fob is in her purse.
One thing I've noticed with fobs is that the system never barks when I've got it in my shirt pocket, but occasionally it has warned when it couldn't find it in my right-side pocket or if I leave it tucked in one of the console areas.
Though, as you say, without getting the normal and customary "fob" warnings, it's hard to imagine the fob is the culprit here.
I did a scan of the owner's manual for your vintage vehicle, but didn't see any mention of a
five-beep warning of that sort. So, I suppose the standard equipment and warnings aren't likely, whereas the tech's sensor suggestion might well be where the problem lies.
I'm a little surprised that the manuals don't seem to list the specific beeping sequence you're experiencing. Though I would fully expect the workshop manuals to do so.
Good luck with the scans at the dealer ... hopefully they'll track it down. Particularly if it's easily duplicated.