feat(nuxt): Inject sentry client config with Nuxt addPluginTemplate

[s1gr1d]

Client-side part of #12760
(to test if size-limit action is complaining)

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser	22.28 KB (0%)
@sentry/browser (incl. Tracing)	33.43 KB (0%)
@sentry/browser (incl. Tracing, Replay)	69.18 KB (0%)
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	62.51 KB (0%)
@sentry/browser (incl. Tracing, Replay with Canvas)	73.24 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback)	85.87 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback, metrics)	87.73 KB (0%)
@sentry/browser (incl. metrics)	26.57 KB (0%)
@sentry/browser (incl. Feedback)	38.93 KB (0%)
@sentry/browser (incl. sendFeedback)	26.9 KB (0%)
@sentry/browser (incl. FeedbackAsync)	31.52 KB (0%)
@sentry/react	25.02 KB (0%)
@sentry/react (incl. Tracing)	36.46 KB (0%)
@sentry/vue	26.39 KB (0%)
@sentry/vue (incl. Tracing)	35.29 KB (0%)
@sentry/svelte	22.41 KB (0%)
CDN Bundle	23.5 KB (0%)
CDN Bundle (incl. Tracing)	35.19 KB (0%)
CDN Bundle (incl. Tracing, Replay)	69.29 KB (0%)
CDN Bundle (incl. Tracing, Replay, Feedback)	74.48 KB (0%)
CDN Bundle - uncompressed	68.97 KB (0%)
CDN Bundle (incl. Tracing) - uncompressed	103.98 KB (0%)
CDN Bundle (incl. Tracing, Replay) - uncompressed	214.38 KB (0%)
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	227.09 KB (0%)
@sentry/nextjs (client)	36.35 KB (0%)
@sentry/sveltekit (client)	34.07 KB (0%)
@sentry/node	150.29 KB (+14.87% 🔺)
@sentry/node - without tracing	85.82 KB (-6.58% 🔽)
@sentry/aws-serverless	112.11 KB (-4.2% 🔽)

[s1gr1d]

Closing this as this was merged here: #12760