Accepted answer
In practice, 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.
Freeze-concentration is the mechanism people miss. As ice forms, everything that is not water is excluded into a shrinking unfrozen fraction, so the local concentration of peptide, buffer salts and preservative rises sharply. If the buffer components crystallise at different rates, local pH can shift by more than a unit. That is why a phosphate-buffered solution can behave badly on freezing while an unbuffered one is fine.
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.
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.
Worth stating: research-use-only material has no stability programme behind it at all, so any beyond-use date you apply is your own construct.
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.