feat(nuxt): Register nuxt route provider

[logaretm]

Registers a route provider for Nuxt in the client plugin, outside the __SENTRY_TRACING__ guard.

Nuxt installs the router before its plugins run, so the plugin can read it straight off nuxtApp rather than waiting for a Vue app the way @sentry/vue has to. Reuses createVueRouteProvider from #23553's successor rather than reimplementing the vue-router resolve handling.

Because it sits outside the tracing guard, route parameterization survives when tracing is tree-shaken away.

Part of #23556

[github-actions]

This pull request has gone three weeks without activity. In another week, I will close it.

But! If you comment or otherwise update it, I will reset the clock, and if you apply the label PR: no-auto-close I will leave it alone ... forever!

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	29.24 kB	-	-
@sentry/browser - with treeshaking flags	27.5 kB	-	-
@sentry/browser - with treeshaking flags tracing without tracing	27.4 kB	-	-
@sentry/browser (incl. Tracing)	51.16 kB	+0.02%	+9 B 🔺
@sentry/browser (incl. Tracing + Span Streaming)	51.18 kB	+0.02%	+8 B 🔺
@sentry/browser (incl. Tracing, Profiling)	54.19 kB	+0.02%	+9 B 🔺
@sentry/browser (incl. Tracing, Replay)	90.77 kB	+0.01%	+8 B 🔺
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	79.87 kB	+0.02%	+9 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	95.47 kB	+0.01%	+7 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback)	108.42 kB	+0.01%	+8 B 🔺
@sentry/browser (incl. Feedback)	46.76 kB	-	-
@sentry/browser (incl. sendFeedback)	34.3 kB	-	-
@sentry/browser (incl. FeedbackAsync)	39.41 kB	-	-
@sentry/browser (incl. Metrics)	30.25 kB	-	-
@sentry/browser (incl. Logs)	30.51 kB	-	-
@sentry/browser (incl. Metrics & Logs)	31.18 kB	-	-
@sentry/react	31 kB	-	-
@sentry/react (incl. Tracing)	53.46 kB	+0.03%	+11 B 🔺
@sentry/vue	37 kB	+0.72%	+261 B 🔺
@sentry/vue (incl. Tracing)	53.86 kB	+0.3%	+159 B 🔺
@sentry/svelte	29.26 kB	-	-
CDN Bundle	30.93 kB	-	-
CDN Bundle (incl. Tracing)	51.7 kB	+0.03%	+12 B 🔺
CDN Bundle (incl. Logs, Metrics)	33.2 kB	-	-
CDN Bundle (incl. Tracing, Logs, Metrics)	53.67 kB	+0.03%	+11 B 🔺
CDN Bundle (incl. Replay, Logs, Metrics)	73.92 kB	-	-
CDN Bundle (incl. Tracing, Replay)	89.29 kB	+0.02%	+9 B 🔺
CDN Bundle (incl. Tracing, Replay, Logs, Metrics)	91.25 kB	+0.01%	+9 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback)	95.46 kB	+0.02%	+11 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics)	97.43 kB	+0.02%	+12 B 🔺
CDN Bundle - uncompressed	91.4 kB	-	-
CDN Bundle (incl. Tracing) - uncompressed	153.81 kB	+0.03%	+41 B 🔺
CDN Bundle (incl. Logs, Metrics) - uncompressed	97.97 kB	-	-
CDN Bundle (incl. Tracing, Logs, Metrics) - uncompressed	159.77 kB	+0.03%	+41 B 🔺
CDN Bundle (incl. Replay, Logs, Metrics) - uncompressed	227.54 kB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	273.54 kB	+0.02%	+41 B 🔺
CDN Bundle (incl. Tracing, Replay, Logs, Metrics) - uncompressed	279.48 kB	+0.02%	+41 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	287.25 kB	+0.02%	+41 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics) - uncompressed	293.17 kB	+0.02%	+41 B 🔺
@sentry/nextjs (client)	56.03 kB	+0.46%	+254 B 🔺
@sentry/sveltekit (client)	51.6 kB	+0.02%	+9 B 🔺
@sentry/core/server	39.96 kB	+0.03%	+11 B 🔺
@sentry/core/browser	13.63 kB	-	-
@sentry/node	133.91 kB	+0.02%	+18 B 🔺
@sentry/node/import (ESM hook with diagnostics-channel injection)	82.43 kB	-	-
@sentry/node - without tracing	90.47 kB	+0.04%	+28 B 🔺
@sentry/node - without channel injection	112.42 kB	+0.02%	+20 B 🔺
@sentry/aws-serverless	98.72 kB	+0.02%	+13 B 🔺
@sentry/cloudflare (withSentry) - minified	206.53 kB	+0.03%	+49 B 🔺
@sentry/cloudflare (withSentry)	513.8 kB	+0.02%	+70 B 🔺

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