Seek is not meant to track your observations. It deliberately doesn’t use user accounts, because it’s directed at children, and meant to be relatively simple. Thus there may not be any external record of your information – it would all be somewhere in the device using Seek.
Depending on where your saved information is kept within your phone, it may be impossible to retrieve. Apparently it is set up so that it can’t be uploaded online (through regular methods, at least).
Have you considered using iNaturalist? It doesn’t have the live identification tools that Seek does, but all your data would be saved online – no need to worry about losing anything when you switch devices.