Seek is designed for people who don’t want to join or log in to a social network like iNaturalist. So you can download Seek, open it up, and you’re good to go to make observations, but they stay on your device only by default. There is no such thing as a Seek account.
The only account you log in to in Seek is an iNaturalist account. The only way to get an observation made in Seek to anywhere else on the internet is to post it to iNaturalist via an iNaturalist account. That iNaturalist account can be a single account you create for your class to post to, which they can all log into via Seek and post to. But that means posting observations to iNaturalist so you’ll have to decide if that’s what you want them to do.
Tjhere is no such thing as a special class account, I’m sorry if that was confusing. What you can do is make an account specifically for your class. It could have a username like “mras_class” or something. But anything posted to that account would be immediately public.