docs(react-router): add sentry init setup

[betegon]

DESCRIBE YOUR PR

Adds the experimental sentry init path to the React Router Framework Mode docs, following the TanStack Start setup pattern. The quick start now points users at npx sentry@latest init, explains how the AI-powered command works, and keeps manual setup as the detailed fallback.

The existing @sentry/wizard command remains available as the non-AI framework wizard path.

This follows the merged TanStack Start docs PR #17693 for the experimental sentry init flow, AI-powered command explanation, and manual-setup fallback pattern.

This also updates the manual setup callout and standardizes React Router Instrumentation API wording on 7.15+.

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TEST PLAN

• git diff --check
• pnpm generate-doctree
• Reviewed final diff to confirm verification/next-step content is restored from base
• Not run: pnpm lint:typos (typos binary unavailable in this checkout)
• Not run: pnpm build (local build requires NEXT_PUBLIC_SENTRY_DSN)

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• Sentry Docs contributor guide

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Project	Deployment	Actions	Updated (UTC)
sentry-docs	Error		Jun 11, 2026 5:51pm

1 Skipped Deployment

Project	Deployment	Actions	Updated (UTC)
develop-docs	Ignored	Preview	Jun 11, 2026 5:51pm

[betegon]

Leaving this note for reviewers: 7.15+ is intentional because the snippets here use the stabilized React Router instrumentation API (instrumentations). React Router 7.9.5 introduced the earlier unstable_* API, so the docs mention it but keep 7.15+ as the minimum for these examples.