fix(react): Set dependency-injected functions as early as possible

[lforst]

Hoping that this may address #12018

We should set these dependency-injections as early as possible.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser	21.65 KB (0%)
@sentry/browser (incl. Tracing)	32.69 KB (0%)
@sentry/browser (incl. Tracing, Replay)	68.03 KB (0%)
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	61.43 KB (0%)
@sentry/browser (incl. Tracing, Replay with Canvas)	72.07 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback)	84.08 KB (0%)
@sentry/browser (incl. Feedback)	37.57 KB (0%)
@sentry/browser (incl. sendFeedback)	26.21 KB (0%)
@sentry/browser (incl. FeedbackAsync)	30.57 KB (0%)
@sentry/react	24.33 KB (0%)
@sentry/react (incl. Tracing)	35.65 KB (+0.02% 🔺)
@sentry/vue	25.48 KB (0%)
@sentry/vue (incl. Tracing)	34.48 KB (0%)
@sentry/svelte	21.77 KB (0%)
CDN Bundle	24.13 KB (0%)
CDN Bundle (incl. Tracing)	34.06 KB (0%)
CDN Bundle (incl. Tracing, Replay)	67.73 KB (0%)
CDN Bundle (incl. Tracing, Replay, Feedback)	72.71 KB (0%)
CDN Bundle - uncompressed	70.98 KB (0%)
CDN Bundle (incl. Tracing) - uncompressed	101.02 KB (0%)
CDN Bundle (incl. Tracing, Replay) - uncompressed	210.64 KB (0%)
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	222.94 KB (0%)
@sentry/nextjs (client)	34.88 KB (0%)
@sentry/sveltekit (client)	33.25 KB (0%)
@sentry/node	147.42 KB (0%)