feat(browser): Remove HttpContext integration class

[Lms24]

Removes the old class-based HttpContext integration in favor of the httpContextIntegration.

(Stumbled upon this while researching something, thought I'd quickly clean it up)

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	76.98 KB (+0.02% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	68.23 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	72.12 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	61.79 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	32.43 KB (-0.04% 🔽)
@sentry/browser (incl. browserTracingIntegration) - Webpack (gzipped)	32.43 KB (-0.04% 🔽)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.36 KB (+0.01% 🔺)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.37 KB (+0.02% 🔺)
@sentry/browser - Webpack (gzipped)	22.55 KB (-0.05% 🔽)
@sentry/browser (incl. Tracing, Replay, Feedback) - CDN Bundle (gzipped)	75.08 KB (-0.02% 🔽)
@sentry/browser (incl. Tracing, Replay) - CDN Bundle (gzipped)	66.69 KB (-0.03% 🔽)
@sentry/browser (incl. Tracing) - CDN Bundle (gzipped)	32.53 KB (-0.05% 🔽)
@sentry/browser - CDN Bundle (gzipped)	24 KB (-0.04% 🔽)
@sentry/browser (incl. Tracing, Replay) - CDN Bundle (minified & uncompressed)	209.02 KB (-0.02% 🔽)
@sentry/browser (incl. Tracing) - CDN Bundle (minified & uncompressed)	97.83 KB (-0.03% 🔽)
@sentry/browser - CDN Bundle (minified & uncompressed)	71.72 KB (-0.03% 🔽)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	68.43 KB (-0.02% 🔽)
@sentry/react - Webpack (gzipped)	22.58 KB (-0.08% 🔽)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	84.94 KB (-0.02% 🔽)
@sentry/nextjs Client - Webpack (gzipped)	49.34 KB (-0.01% 🔽)
@sentry-internal/feedback - Webpack (gzipped)	17.41 KB (0%)