Acquire a domain (labs) — find and buy through Convex

Suggest memorable names for the idea, check live availability + price, then (only on explicit yes) register the chosen domain through Convex and bind it to the deployment.

Workflow

1. Brainstorm a few on-theme names; check live availability + annual price.
2. Present the top options with prices; wait for an explicit pick.
3. Register through Convex (DNSimple) — a Tier-2 spend action performed by the control plane; the agent never holds the registrar credential.
4. Point DNS at the deployment and attach it as a Convex custom domain; rebind the auth origin (RP_ID/ORIGIN) and re-publish.

Rules

• Never register without an explicit yes on a specific domain.
• Show the price before registering.
• If the user already owns a domain, hand off to the domains capability instead of buying a new one.
• Rebinding the domain changes the auth origin — re-publish after.