Accepted answer
The lyophilised solid is far more robust than anything anyone says about it, and the solution is far less robust. Most of the confusion in this area comes from advice about one being applied to the other.
Light matters for specific residues rather than in general. Tryptophan and to a lesser extent tyrosine and methionine are photo-labile; a sequence without them is largely indifferent to ambient light over the timescales in question. Amber glass is cheap insurance rather than a requirement.
Specifically, practical thermal arithmetic for a shipment: a single 250 g phase-change pack in a thin-walled polystyrene box holds sub-ten-degrees for roughly 24 to 48 hours in a 25 °C ambient, and considerably less at 35 °C. Any lane taking eight to fourteen days is therefore not temperature-controlled for most of its duration regardless of what was in the box, which is the argument for shipping the material lyophilised.
The licensed semaglutide and tirzepatide presentations carry in-use periods of several weeks at room temperature in their labelling, which is the closest thing to real stability data in this space — and it applies to a buffered, surfactant-containing, preservative-containing formulation, not to a reconstituted research vial.
One qualification: none of this addresses sterility. A vial can be chemically pristine and microbiologically compromised, and a chromatogram will not tell you which.
The single highest-value change most people can make is buying a cheap logging thermometer, because it converts an assumption about their storage into a record.