>..do magnetic platters offer longer lasting data integrity than SSDs in cold storage?

Yes. With an SSD the enemy is electron leakage. Minute quantities of electrons trying to escape an unnatural state and return to equilibrium. (yes, I just anthropomorphized electrons.) Magnets however are more stable by nature. (yes there is nothing natural about hard-drive storage. SMR doubly so!)

Anecdote/anecdata: I have been able to retrieve full drives worth of data off of drives that have sat in a cardboard box for 10 years. I also have trouble accessing data on 1-year old USB flash drives.

The JEDEC standard specifies client SSDs have to retain data powered off for a year under worst case temperature. Enterprise drives have a relaxed requirement for three months. This is because lower programming voltages are used to achieve higher total bytes written endurance.

Even hard disks should be powered on occasionally to test backups.

In general I trust the older tech more than newer for long-term archiving. So that would mean HDD (the oldest tech thereof you can find still sold, probably) or tape or DVD over SSD.

But multiple copies in multiple formats cannot hurt, and the most important stuff should have multiple live copies.

I've been coming around to the POV that "cold storage" is a bad idea and it's best to keep everything hot. It's been discussed on 2.5admins.com a lot.

Not sure about that but I do know that the new sealed helium filled drives are much harder to take apart and do backup recovery on