you can use an android firewall to block Internet access from the app
True, however, AFAIK if your phone is not rooted, you can't have a firewall and VPN running at the same time (the firewalls I've seen must be configured as VPN).
not the privileges that obsidian has
Also true, although Obsidian has access to that shared storage, and therefore, Obsidian being closed source, you have no way of knowing what they do with the files other apps create in that storage directory. I'm not saying they are acting maliciously, but I don't like this approach (software vulnerabilities, supply chain attacks, etc.). The devs recognized the issue in another thread, but there's no solution to the problem as of yet.
Obsidian asks for the permission upon first launch, but if you don't give it access it won't work at all (it's a required permission for the app).