I've been searching and I think there's no ability to do this. Vanadium on Android and chromium on desktop do not have logins, and you can't add extensions to Vanadium. So it's a no go.
You will have to share the URL text over some other service like Easyjoin ($18.99) or Keep or some other syncing note service.
I might just switch back to Firefox or Opera and only use Vanadium for situations I'm concerned about a private non-tracking browser connection.