Part of #9807.
Support adding a completed render back to the virtual public folder as an asset in Browser Studio on remotion.dev/new. Browser Studio uses the client-side WebCodecs render path; the resulting file should be addable to the virtual public folder.
Requirements
- Implement the action as a typed Browser Studio operation against the virtual project. Do not mock the HTTP API.
- The action is backed by an explicit Browser Studio capability and is hidden or disabled when unavailable.
- Mutations update the virtual project, trigger HMR, and participate in undo/redo where applicable.
- Browser Studio tests cover the successful action and structured failure cases.