Right now, Vanadium doesn’t support being backed up by Seedvault because it’s a system app without the required backup hooks, so browser data won’t transfer that way. Modifying the manifest might enable backup support, but because Vanadium is a system app with tight security and sandboxing, it’s not as simple as a sideload, it would require a build change by the maintainers.
If this capability is important to you, the best path is to engage with the official issue thread and/or offer a bounty to developers who can implement proper backup support upstream. Nothing ready-made exists yet, but active interest can help prioritize it.