fix(v10/cloudflare): Use gen_ai.agent.name for class names

[JPeer264]

Backport of: #22911

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	27.75 kB	added	added
@sentry/browser - with treeshaking flags	26.19 kB	added	added
@sentry/browser (incl. Tracing)	46.6 kB	added	added
@sentry/browser (incl. Tracing + Span Streaming)	48.38 kB	added	added
@sentry/browser (incl. Tracing, Profiling)	51.34 kB	added	added
@sentry/browser (incl. Tracing, Replay)	85.84 kB	added	added
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	75.48 kB	added	added
@sentry/browser (incl. Tracing, Replay with Canvas)	90.55 kB	added	added
@sentry/browser (incl. Tracing, Replay, Feedback)	103.2 kB	added	added
@sentry/browser (incl. Feedback)	44.92 kB	added	added
@sentry/browser (incl. sendFeedback)	32.55 kB	added	added
@sentry/browser (incl. FeedbackAsync)	37.68 kB	added	added
@sentry/browser (incl. Metrics)	28.84 kB	added	added
@sentry/browser (incl. Logs)	29.07 kB	added	added
@sentry/browser (incl. Metrics & Logs)	29.76 kB	added	added
@sentry/react	29.55 kB	added	added
@sentry/react (incl. Tracing)	48.86 kB	added	added
@sentry/vue	33.17 kB	added	added
@sentry/vue (incl. Tracing)	48.56 kB	added	added
@sentry/svelte	27.78 kB	added	added
CDN Bundle	30.14 kB	added	added
CDN Bundle (incl. Tracing)	48.56 kB	added	added
CDN Bundle (incl. Logs, Metrics)	31.73 kB	added	added
CDN Bundle (incl. Tracing, Logs, Metrics)	49.86 kB	added	added
CDN Bundle (incl. Replay, Logs, Metrics)	70.99 kB	added	added
CDN Bundle (incl. Tracing, Replay)	86.05 kB	added	added
CDN Bundle (incl. Tracing, Replay, Logs, Metrics)	87.36 kB	added	added
CDN Bundle (incl. Tracing, Replay, Feedback)	91.86 kB	added	added
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics)	93.12 kB	added	added
CDN Bundle - uncompressed	89.9 kB	added	added
CDN Bundle (incl. Tracing) - uncompressed	146.78 kB	added	added
CDN Bundle (incl. Logs, Metrics) - uncompressed	94.61 kB	added	added
CDN Bundle (incl. Tracing, Logs, Metrics) - uncompressed	150.75 kB	added	added
CDN Bundle (incl. Replay, Logs, Metrics) - uncompressed	219.37 kB	added	added
CDN Bundle (incl. Tracing, Replay) - uncompressed	266.01 kB	added	added
CDN Bundle (incl. Tracing, Replay, Logs, Metrics) - uncompressed	269.98 kB	added	added
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	279.71 kB	added	added
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics) - uncompressed	283.67 kB	added	added
@sentry/nextjs (client)	51.4 kB	added	added
@sentry/sveltekit (client)	47.02 kB	added	added
@sentry/core/server	80.44 kB	added	added
@sentry/core/browser	66.78 kB	added	added
@sentry/node-core	63.25 kB	added	added
@sentry/node	125.89 kB	added	added
@sentry/node (incl. diagnostics channel injection)	151.33 kB	added	added
@sentry/node/import (ESM hook with diagnostics-channel injection)	70.03 kB	added	added
@sentry/node/light	51.41 kB	added	added
@sentry/node - without tracing	74.94 kB	added	added
@sentry/aws-serverless	84.21 kB	added	added
@sentry/cloudflare (withSentry) - minified	200.5 kB	added	added
@sentry/cloudflare (withSentry)	492.68 kB	added	added