Trulicity

Trulicity contains GLP-1 agonist, so it mimics the actions of Glucagon. (confusingly not actually Glucagon, but another hormone called Glucagon-like Peptide 1).

So - It doesn't directly slow down your metabolism, but it does slow down the rate your stomach empties, and increases insulin production too. All of that should result in lower, slower rises in blood glucose for any given meal, and a longer feeling of being satisfied.

If someone was equating "metabolism" to "digestion" - I could see that being a thing someone might say, but to my knowledge metabolism shouldn't be affected.

I have no personal experience myself - though lots of people seem to be having success.

To answer your question - you would really need to use a CGM or take multiple readings to figure out what the effect is for you...

He stole your phone, and threw it in the canal - as a form of protest? - wow, that's a new one....
Presumably he wouldn't get the joke if someone threw him in the canal....