React DevTools "Error rendering inspected element" in AppRoute

### Prerequisites

- [x] I have written a descriptive issue title
- [x] I have searched existing issues to ensure the bug has not already been reported

### Fastify version

5.5.0

### Plugin version

8.2.0

### Node.js version

24.6.0

### Operating system

Linux

### Operating system version (i.e. 20.04, 11.3, 10)

Fedora Linux 42 (Cinnamon) x86_64

### Description

I used the react-base starter from: giget gh:fastify/fastify-vite/starters/react-base#dev your-app

The issue seems to only occur when the client/pages/index.jsx component has `getData` or `getMeta` functions in it.
Maybe React Dev Tools breaks because these functions are server-side, so this isn't a fastify/vite issue then?

When inspecting the AppRoute component in React Developer Tools
6.1.5, the console shows a ReactDebugToolsRenderError: Error rendering
inspected component with an underlying Promise {} error. This error seems to be related to a useEffect hook and
possibly the use of valtio for state management within the component. The error does not occur if the useEffect hook at line
76 of @fastify/react/virtual/core.jsx is commented out.

Console Error:

1 backendManager.js:1 Error rendering inspected element.
2
3 ReactDebugToolsRenderError: Error rendering inspected component
4 at handleRenderFunctionError (react-debug-tools.production.js:759:24)
5 at inspectHooks (react-debug-tools.production.js:775:5)
6 at t.inspectHooksOfFiber (react-debug-tools.production.js:867:12)
7 at renderer.js:4269:17
8 at inspectElementRaw (renderer.js:4110:14)
9 at Object.inspectElement (renderer.js:4731:38)
10 at agent.js:495:18
11 at Bridge.emit (events.js:37:18)
12 at bridge.js:298:23
13 at listener (backendManager.js:1:12649)

1 backendManager.js:1 React DevTools encountered an error while trying to inspect hooks. This is most likely caused by
an error in current inspected component: "AppRoute".
2 The error thrown in the component is:
3
4 Promise {}

Steps to Reproduce

1. Run the development server (npm run dev).
2. Open the application in Google Chrome (http://localhost:3000).
3. Open React DevTools.
4. Inspect the AppRoute component.
5. Observe the error in the browser's developer console.

I used gemini-2.5-pro to try find the problem. Below is what it tried, with no success:
Troubleshooting Steps Taken

1. Exhaustive Dependencies: Added ctx and ctxHydration to the useEffect dependency array. This did not resolve the issue.
2. `setTimeout`: Wrapped the body of the useEffect in a setTimeout(..., 0) to defer execution. This did not resolve the issue.
3. Memoize `valtio` Proxy: Used useState to memoize the valtio proxy object created for the RouteContext.Provider. This did not
resolve the issue.

Ignore the `override` in `package.json`. There was a deprecation warning that I wanted to rule out from my testing of the issue.

### Link to code that reproduces the bug

https://github.com/nofxboy1234/your-app

### Expected Behavior

The AppRoute component should be inspectable in React DevTools without throwing an error.