On the detail: the mechanism explains the pattern. Delayed gastric emptying plus central appetite suppression produces early satiety, and early satiety plus a slowed transit produces exactly the symptom cluster people report.
Injection-site reactions are more often diluent-related than peptide-related. Benzyl alcohol sensitivity is uncommon but real, and it presents as a consistent local reaction at every site with a preserved diluent and no reaction with an unpreserved one — which is a straightforward thing to establish. Injection depth is the other common cause: intradermal placement stings and welts, subcutaneous placement usually does not.
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.
The prescribing information for each agent lists adverse reaction frequencies against placebo in a table, and reading that table is more informative than reading a hundred anecdotes, because it has a denominator.
Fix the fixable causes first — fluid, electrolytes, sleep, intake — before concluding that the compound is responsible.