Pinning this issue since it seems to get asked once every week.

The pets must live inside a panel because this is how the VS Code Extensions work.

IF you want custom graphics that aren't text (e.g. little cats and dogs), they must live within a web panel. This panel has to be a tab inside the editor, or on the explorer.

So no, it's not possible. If it becomes possible, I'll unpin this issue and work on it.