I approved this feature request and meant to add some clarifications right afterward but got distracted. Sorry!
Here’s a previous statement I made about this kind of functionality.
As noted, Seek is really focused on privacy and not sharing information. So it’s unlikely we’d sync between devices if “sync” means that if you had Seek installed on two different devices they’d both instantly sync the same observations (and achievements) between them.
For the specific situation @jacobpants mentioned - getting a new device and wanting to transfer your existing observations to it - I think some sort of manual backup option is more likely. You could choose to back up your observations to some cloud storage and then, when you install Seek on your new device, you could download those from the backup. One issue, of course, is that Seek is built for privacy and iNat not storing your information, so uploading all this to iNat’s servers would be a bit antithetical to that.
What I think might work is just making sure Seek data is stored in backups of devices. iOS devices already do this. If you back up your iPhone/iPad to either iCloud to your computer and restore your new device from that backup, your Seek observations will be part of that backup. I recently lost my iPhone in San Francisco Bay and, when I restored my new phone from that older phone’s backup, all my Seek observations were in it, so in my experience it worked well.
I think doing this for Android is a bit more tricky (we’ve explored it a bit) but I’d love to see that happen. It’s a bummer to lose your observations just because you got a new phone.