Start by separating chemical degradation from physical degradation, because they fail differently and they are detected differently. Chemical degradation changes the molecule and shows up as new peaks on a chromatogram. Physical degradation aggregates the molecule and often shows up as nothing at all on reverse-phase HPLC, because the aggregate never makes it onto the column.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle. If it arrived as a solution that thawed, re-freezing adds a second transition and therefore a second dose of ice-front shear. The asymmetry is worth internalising.
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.
If the material arrived warm and it was lyophilised, test it and proceed on the result. If it arrived warm and it was in solution, the result is more likely to be interesting than reassuring.