Remote storage is backup. Your AnyType content is held locally - on your devices.
If you exceed the 1GB limit, then less of your data will be backed up to remote storage, but that does not affect your data on your devices. And you can back up your AnyType local data whenever you want either automatically if you have specialist backup software, or via exports.
AnyType is local first - local is where your data is kept and belongs.
Also, as the team has pointed out, unless you store large volumes of video and audio in AnyType, you are extremely unlikely to it the 1GB limit.
To clarify further, back-up storage only applies to files (like audio, video, images or pdfs), not Objects or their content. If you’re only using images and text, 1GB will be more than enough. There is no limit to how many files added to the local instance of Anytype on your device, so as long as you’re on the same network, p2p sync will work regardless of what is stored in the back-up node.
The back-up node exists to facilitate sync and preserve changes when you’re working remotely. It’s also handy if you need to log in to a new device and want to restore your entire account. If anything happens to your device, all your work is safe in the encrypted back up node.