Answering this needs the distinction between the native hormone and the pharmacological agents, whose half-lives differ by three orders of magnitude and whose effects therefore differ in kind.
Albumin binding does the rest of the work. A fatty-acid chain attached through a linker binds circulating albumin reversibly, which both shields the peptide from renal clearance and creates a depot; that is how a two-minute hormone becomes a once-weekly drug.
Concretely, central effects reach the arcuate nucleus and the area postrema, regions with an incomplete blood-brain barrier. That anatomy is why a large peptide can act centrally at all, and it also explains the nausea, since the area postrema is the chemoreceptor trigger zone.
Area postrema involvement in nausea from this class is supported by lesion studies in animals and by the anatomy of the circumventricular organs.
A receptor being expressed in a tissue does not establish that activating it there matters at therapeutic exposures.
Nausea and appetite share an anatomy, which is why they are hard to separate by dose.
edited 26 Oct 2025 by nine_point_nine — reworded for clarity after a comment