More usefully, the honest framing is that this is very common, usually self-limiting, and occasionally the presentation of something that is not self-limiting at all — and the differentiating features are specific enough to be worth knowing.
Constipation outlasts the nausea because it has two causes and only one of them resolves. Gastric emptying accommodates over weeks; total intake, and therefore stool volume and the osmotic load reaching the colon, does not recover until intake does. This is why fibre alone can make it worse — you add bulk to a system that is short of water and short of motility.
Specifically, early satiety is not a side effect; it is the mechanism being observable. The useful distinction is between satiety, where you stop eating without distress, and aversion, where the thought of food is unpleasant. The first is the intended effect. The second frequently precedes the dose being too high or escalated too fast.
Pooled analyses of gallbladder-related events with GLP-1 receptor agonists find a modest increase in relative risk, with the effect larger at higher doses and longer durations — consistent with a rate-of-loss mechanism as much as a direct one[1].
The limitation of the timing heuristic is that it works well for common events and poorly for rare ones, which are precisely the ones that matter most.
If the timing does not fit the escalation, look for another explanation before settling on the drug.