Rename the dashboard program castle-app -> castle

The dashboard is now served at castle.<domain> (was castle-app.<domain>). Since
the subdomain is the program name, this is just a program rename plus the one
special-case constant.

- Generator: _DASHBOARD = "castle" (the :9000 redirect target and off-mode root).
- Program file renamed (runtime): programs/castle-app.yaml -> programs/castle.yaml
  (source unchanged: repo:app).
- Dashboard UI: ProgramDetail shows a frontend's subdomain (via subdomainUrl),
  dropping the old castle-app-at-root special-case; comment refs updated.
- Docs: registry.md/design.md/react-vite.md updated to the subdomain model and the
  `castle` name (react-vite.md also corrected — frontends serve at their subdomain
  root with VITE_BASE=/, and builds are manual via `castle program build`, not
  deploy).

app/src/lib/labels.ts

@@ -50,7 +50,7 @@ export function stackLabel(stack: string): string {
 
 /**
  * Full URL for a service exposed at <subdomain>.<gateway.domain>. The domain is
- * derived from the dashboard's own host (it is served at castle-app.<domain>), so
+ * derived from the dashboard's own host (it is served at castle.<domain>), so
  * this returns null when the dashboard is on a bare host (off mode, no subdomains).
  */
 export function subdomainUrl(subdomain: string): string | null {

app/src/pages/ProgramDetail.tsx

@@ -1,7 +1,7 @@
 import { useState } from "react"
 import { useParams } from "react-router-dom"
 import { useProgram, useEventStream } from "@/services/api/hooks"
-import { runnerLabel } from "@/lib/labels"
+import { runnerLabel, subdomainUrl } from "@/lib/labels"
 import { DetailHeader } from "@/components/detail/DetailHeader"
 import { ConfigPanel } from "@/components/detail/ConfigPanel"
 import { DeploymentsSection } from "@/components/detail/DeploymentsSection"
@@ -28,14 +28,12 @@ export function ProgramDetailPage() {
     )
   }
 
-  // A static frontend (frontend behavior, build outputs, no service) is served
-  // by the gateway in place — show where.
+  // A static frontend (frontend behavior, build outputs, no service) is served by
+  // the gateway in place at its own subdomain — show where.
   const buildOutputs = (deployment.manifest.build as { outputs?: string[] } | undefined)?.outputs
   const servedAt =
     deployment.behavior === "frontend" && deployment.services.length === 0 && buildOutputs?.length
-      ? deployment.id === "castle-app"
-        ? "/"
-        : `/${deployment.id}/`
+      ? (subdomainUrl(deployment.id) ?? `${deployment.id}.<gateway.domain>`)
       : null
 
   return (

app/src/services/api/client.ts

@@ -1,5 +1,5 @@
 // Resolve the castle-api base URL. The gateway serves each service at its own
-// subdomain (<name>.<domain>), so when the dashboard runs at castle-app.<domain>
+// subdomain (<name>.<domain>), so when the dashboard runs at castle.<domain>
 // the API lives at castle-api.<domain> — a cross-origin call (castle-api allows
 // CORS *). When served at a bare host (dev, or the off-mode :9000 gateway), the
 // API is reachable same-origin at /api.