Support lazy-loading to keep the initial client bundle small (@sentry/nuxt)

### Problem Statement

The legacy Nuxt 2 module `@nuxtjs/sentry` exposed a `[lazy: true` option](https://sentry.nuxtjs.org/guide/lazy-loading/) that:
- removed the Sentry runtime from the default client bundle
- injected a mocked `$sentry` instance together with `$sentryReady()` / `$sentryLoad()` helpers so we could load Sentry on-demand (e.g. after user consent or on the first error)

In production this shaved 40 kB (gzipped) off the initial JS sent to every visitor, important for Core Web Vitals on mobile connections.

The current Nuxt 3 integration always ships the full SDK in the main bundle. For apps that need the SDK only after explicit user consent or once the user is authenticated this is avoidable overhead.

### Solution Brainstorm

It would be great if `@sentry/nuxt` could bring back first-class lazy-loading support, for example:

1. **Config flag**
```ts
// nuxt.config.ts
sentry: { lazy: true, /* … */ }
```

2. **Mocked API injection** (parity with Nuxt 2)
* Inject a lightweight proxy that queues calls until the real SDK is loaded.
* Expose `$sentryReady()` (Promise) and optionally `$sentryLoad()` to manually trigger the load.

3. **Route-level auto-loading**
Allow opting into SDK loading per-route via route rules or middleware so that public/landing pages remain lean.

4. **Vite split-chunk**
Generate a separate `sentry.client.js` chunk and load it dynamically so source-maps & release artifacts continue to work as today.

Start by reviewing the current @sentry/nuxt integration alongside the legacy Nuxt 2 lazy-loading behavior described in the linked documentation. Use nuxt.config.ts, route rules or middleware, and the Vite split-chunk approach as the proposed integration points. Done should include an opt-in lazy mode that keeps the initial client bundle small while preserving the requested loading and mocked API behavior.

Written by the indexing model from the issue text.