Originally posted by Fzanco:

It's all saved server side. I was able to install on another computer and pick my game with no interruptions

Originally posted by Aldo:

Everything is local.... back up your files
https://www.ign.com/wikis/valheim/How_to_Back_Up_Your_Save_Data

Yes and no.
Valheim indeed keep its save files at the Steam Cloud, but I'm not sure how exactly rules for cloud save restoration work.
While it is advised to backup anyway, I'd say some of your saves are definitely held at the Steam Cloud.