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	29.51 kB	+0.51%	+148 B 🔺
@sentry/browser - with treeshaking flags	27.68 kB	+0.13%	+34 B 🔺
@sentry/browser - with treeshaking flags tracing without tracing	27.58 kB	+0.14%	+38 B 🔺
@sentry/browser (incl. Tracing)	51.46 kB	+0.31%	+154 B 🔺
@sentry/browser (incl. Tracing + Span Streaming)	51.47 kB	+0.3%	+149 B 🔺
@sentry/browser (incl. Tracing, Profiling)	54.47 kB	+0.31%	+164 B 🔺
@sentry/browser (incl. Tracing, Replay)	91.05 kB	+0.18%	+155 B 🔺
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	80.03 kB	+0.05%	+36 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	95.73 kB	+0.16%	+150 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback)	108.72 kB	+0.14%	+149 B 🔺
@sentry/browser (incl. Feedback)	47.04 kB	+0.33%	+154 B 🔺
@sentry/browser (incl. sendFeedback)	34.57 kB	+0.42%	+144 B 🔺
@sentry/browser (incl. FeedbackAsync)	39.69 kB	+0.37%	+143 B 🔺
@sentry/browser (incl. Metrics)	30.53 kB	+0.51%	+153 B 🔺
@sentry/browser (incl. Logs)	30.82 kB	+0.5%	+152 B 🔺
@sentry/browser (incl. Metrics & Logs)	31.48 kB	+0.47%	+147 B 🔺
@sentry/react	31.36 kB	+0.53%	+165 B 🔺
@sentry/react (incl. Tracing)	53.82 kB	+0.29%	+153 B 🔺
@sentry/vue	37.51 kB	+1.65%	+607 B 🔺
@sentry/vue (incl. Tracing)	54.36 kB	+0.89%	+476 B 🔺
@sentry/svelte	29.54 kB	+0.5%	+146 B 🔺
CDN Bundle	31.22 kB	+0.13%	+39 B 🔺
CDN Bundle (incl. Tracing)	51.99 kB	+0.08%	+41 B 🔺
CDN Bundle (incl. Logs, Metrics)	33.46 kB	+0.1%	+31 B 🔺
CDN Bundle (incl. Tracing, Logs, Metrics)	53.94 kB	+0.1%	+49 B 🔺
CDN Bundle (incl. Replay, Logs, Metrics)	74.2 kB	+0.07%	+49 B 🔺
CDN Bundle (incl. Tracing, Replay)	89.56 kB	+0.04%	+34 B 🔺
CDN Bundle (incl. Tracing, Replay, Logs, Metrics)	91.54 kB	+0.05%	+45 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback)	95.73 kB	+0.04%	+33 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics)	97.73 kB	+0.07%	+60 B 🔺
CDN Bundle - uncompressed	92.14 kB	+0.11%	+95 B 🔺
CDN Bundle (incl. Tracing) - uncompressed	154.53 kB	+0.07%	+95 B 🔺
CDN Bundle (incl. Logs, Metrics) - uncompressed	98.71 kB	+0.1%	+95 B 🔺
CDN Bundle (incl. Tracing, Logs, Metrics) - uncompressed	160.48 kB	+0.06%	+95 B 🔺
CDN Bundle (incl. Replay, Logs, Metrics) - uncompressed	228.28 kB	+0.05%	+95 B 🔺
CDN Bundle (incl. Tracing, Replay) - uncompressed	274.26 kB	+0.04%	+95 B 🔺
CDN Bundle (incl. Tracing, Replay, Logs, Metrics) - uncompressed	280.2 kB	+0.04%	+95 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	287.96 kB	+0.04%	+95 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics) - uncompressed	293.89 kB	+0.04%	+95 B 🔺
@sentry/nextjs (client)	56.32 kB	+0.74%	+413 B 🔺
@sentry/sveltekit (client)	51.88 kB	+0.29%	+145 B 🔺
@sentry/core/server	39.99 kB	-	-
@sentry/core/browser	13.63 kB	-	-
@sentry/node	144.03 kB	+0.01%	+8 B 🔺
@sentry/node/import (ESM hook with diagnostics-channel injection)	82.98 kB	-	-
@sentry/node - without tracing	92.91 kB	+0.01%	+8 B 🔺
@sentry/node - without channel injection	122.41 kB	+0.01%	+9 B 🔺
@sentry/aws-serverless	101.17 kB	-0.01%	-10 B 🔽
@sentry/cloudflare (withSentry) - minified	206.69 kB	-	-
@sentry/cloudflare (withSentry)	514.13 kB	-	-

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