The part that matters: 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.
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.
Worth being precise here: 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.
Deamidation kinetics for asparagine in peptides are well characterised and strongly sequence-dependent: the residue following the asparagine dominates the rate, with glycine and serine at the n+1 position accelerating it by an order of magnitude relative to bulkier residues. That is why two peptides in the same buffer at the same temperature can have quite different shelf lives.
I would be careful about generalising across sequences. Stability is sequence-specific, and a rule derived from semaglutide will not transfer cleanly to a tri-agonist with different residues in different local environments.
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.