Answer first: the gastrointestinal effects in this class share one mechanism — slowed gastric emptying plus central signalling — and present as nausea, fullness, reflux, constipation or diarrhoea depending on the person.
Fat is the macronutrient that slows emptying most on its own, so a high-fat meal on top of pharmacologically delayed emptying is the combination that produces the worst episodes.
Discontinuation for gastrointestinal effects in the trials runs in the low single-figure percentages, which means the great majority of people who experience these effects continue.
The caveat is that severe persistent symptoms, particularly with dehydration or severe pain, are clinical and not a matter of waiting them out.
Slow the titration first. It is the intervention with the best evidence and the lowest cost.