In contrast to Dropbox, you can have as many shared folders as you want, so you don’t have to use .stignore to sync only specific files / folders to specific devices. But if only one device has all shared folders, that one needs to be powered on and connected for the other devices to be able to send / receive changes.
Syncthing itself is a sync tool, so if you “use it to access documents from” you phone, you will either have to sync the folder and maybe use .stignore to sync only what you want on your phone, or use Syncthing Lite to access files on demand.