Freeze-thaw damage happens at the moving ice front, not at the storage temperature. Once the sample is frozen solid and cold, very little is happening. The damage is done during freezing and thawing, which is why the number of cycles matters and the duration of the hold mostly does not.
The 28-day figure for a reconstituted preserved vial is microbiological, not chemical. Chemically, a well-behaved peptide at 5 mg/mL at 4 °C will typically lose well under a per cent of content per month. The reason to respect the date is bioburden, and bioburden is a function of how many times you have opened it, not of the calendar.
A domestic freezer holds roughly minus eighteen degrees and cycles by several degrees on its defrost schedule, which for a lyophilised solid is entirely adequate and for a frozen solution means repeated partial melting at the surface. If you are going to freeze a solution, an unopened chest freezer is materially better than the compartment in the top of a fridge.
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.
The caveat is that "within specification" and "unchanged" are different claims. A vial can lose a few per cent of content and still be usable for its purpose while no longer matching its certificate.
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.