feat(registry): bring back the video-primitive moves (#3169)

Restores the 208 catalog items reverted after their previews 404'd in
production, this time on the payload mechanism rather than the .html files
that caused the outage.

The generator no longer writes a preview document to docs/public. That writer,
and the machinery under it, existed only to produce files the docs host
discards, so it is gone rather than bypassed. Items now embed the composition
itself via a payload, which is what the previous change already does for the
items that were already in the catalog.

The variables explorer is parked, not restored: it drove its preview through
the same unpublished .html path, so it would have shown an empty frame. Items
that declare variables get the live player plus the static variables table, and
reconnecting the explorer to payloads is a follow-up.

registry/components/badge-pop/registry-item.json

@@ -0,0 +1,79 @@
+{
+  "$schema": "https://hyperframes.heygen.com/schema/registry-item.json",
+  "name": "badge-pop",
+  "type": "hyperframes:component",
+  "title": "Badge Pop",
+  "description": "A transitions.dev-inspired notification badge pop with elastic scale and count reveal",
+  "tags": [
+    "video-primitive",
+    "transition-primitive",
+    "transitions-dev-port",
+    "badge",
+    "microinteraction"
+  ],
+  "files": [
+    {
+      "path": "badge-pop.html",
+      "target": "compositions/components/badge-pop.html",
+      "type": "hyperframes:snippet"
+    }
+  ],
+  "variables": [
+    {
+      "id": "count",
+      "type": "string",
+      "role": "style",
+      "label": "Count",
+      "description": "Text shown inside the notification badge, up to four characters.",
+      "default": "3",
+      "maxLength": 4
+    },
+    {
+      "id": "accent",
+      "type": "enum",
+      "role": "style",
+      "label": "Accent",
+      "description": "Colour family of the badge.",
+      "default": "red",
+      "options": [
+        {
+          "value": "red",
+          "label": "Red"
+        },
+        {
+          "value": "blue",
+          "label": "Blue"
+        },
+        {
+          "value": "green",
+          "label": "Green"
+        },
+        {
+          "value": "violet",
+          "label": "Violet"
+        }
+      ]
+    },
+    {
+      "id": "surface",
+      "type": "enum",
+      "role": "style",
+      "label": "Surface",
+      "description": "Chrome of the button and the badge ring: light for bright frames, dark for dark ones.",
+      "default": "light",
+      "options": [
+        {
+          "value": "light",
+          "label": "Light"
+        },
+        {
+          "value": "dark",
+          "label": "Dark"
+        }
+      ]
+    }
+  ],
+  "preview": {
+    "poster": "https://static.heygen.ai/hyperframes-oss/docs/images/catalog/components/badge-pop.png"
+  }
+}