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.
Glucagon suppression is also glucose-dependent and is lost during hypoglycaemia, which preserves the counter-regulatory response — a genuinely elegant piece of physiology and the reason the class is safe in this respect.
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.
The position-8 substitution conferring DPP-4 resistance appears in essentially every long-acting agent in the class, which is about as strong a piece of convergent evidence as medicinal chemistry offers.
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.