Since you have a nurse in the family, I assume they've not yet run across the usual warnings.
For anyone scrolling by, it's very common to start with a one month supply of the lowest dose of a given glp modifier. It determines tolerance for the meds with less risk, and starts the process of ramping it up to the eventual treatment dose. You'd only get a recurring prescription once you and your provider determine what dosage is optimum.
But the energy drink thing is about the gastrointestinal side effects.
Glp drugs' most common side effect is digestive disturbances. Nausea, constipation and/or diarrhea, reflux/heartburn, all of which may or may not occur with pain or other distress.
Since energy drinks are high in caffeine and sugar, they are known to aggravate those symptoms. They do it without any other factors, but on a glp based med, it gets way worse.
The nausea increase tends to come from the harsh sugar spike to the system, and the insulin dump that follows. However, the drugs themselves can cause it without any other factors.
Intestinal disturbances come from multiple factors, but largely from the way the various options shift intestinal motility. Very commonly, you'll see a cycle of constipation followed by a wave of diarrhea as the bowel counters it by adding water to things. The constipation breaks loose, and then pppbbbbttthhhbbbpppsshhhhhhhht. Sometimes for a few hours from what I've been told.
Reflux is predominantly just an aggravation of preexisting reflux due to the way stomach acids and the valve that closes the stomach off are working, with caffeine making it significantly worse. However, even in patients with no preexisting reflux, it can happen, and is (again) more likely with caffeine intake of significant levels.
Overall, if you need caffeine due to addiction or maladaptive use, go with things that give a lower dose. If needed, increase frequency of dose rather than higher single doses. A dozen cups of tea across the day is less problematic than a red bull once.