fix(internal): Remove deprecated JS SDK code

[krystofwoldrich]

📢 Type of change

• Bugfix
• New feature
• Enhancement
• Refactoring

📜 Description

💡 Motivation and Context

💚 How did you test it?

📝 Checklist

• I reviewed submitted code
• I added tests to verify changes
• No new PII added or SDK only sends newly added PII if sendDefaultPII is enabled
• All tests passing
• No breaking changes

🔮 Next steps

[github-actions]

	Fails
🚫	Please consider adding a changelog entry for the next release.

Instructions and example for changelog

Please add an entry to CHANGELOG.md to the "Unreleased" section. Make sure the entry includes this PR's number.

Example:

## Unreleased

- Remove deprecated JS SDK code ([#3576](https://github.com/getsentry/sentry-react-native/pull/3576))

If none of the above apply, you can opt out of this check by adding #skip-changelog to the PR description.

Generated by 🚫 dangerJS against 0c01575

[github-actions]

Android (legacy) Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	475.36 ms	502.56 ms	27.20 ms
Size	17.73 MiB	19.93 MiB	2.20 MiB

Previous results on branch: kw-fix-deprecations

Startup times

Revision	Plain	With Sentry	Diff
56d9dcc	407.08 ms	438.22 ms	31.14 ms

App size

Revision	Plain	With Sentry	Diff
56d9dcc	17.73 MiB	19.90 MiB	2.17 MiB

[github-actions]

iOS (legacy) Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	1202.57 ms	1203.63 ms	1.06 ms
Size	2.36 MiB	2.92 MiB	569.53 KiB

Previous results on branch: kw-fix-deprecations

Startup times

Revision	Plain	With Sentry	Diff
56d9dcc+dirty	1241.27 ms	1246.61 ms	5.35 ms

App size

Revision	Plain	With Sentry	Diff
56d9dcc+dirty	2.36 MiB	2.90 MiB	552.83 KiB

[github-actions]

iOS (new) Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	1235.91 ms	1242.73 ms	6.82 ms
Size	2.92 MiB	3.48 MiB	575.08 KiB

Previous results on branch: kw-fix-deprecations

Startup times

Revision	Plain	With Sentry	Diff
56d9dcc+dirty	1236.80 ms	1237.98 ms	1.17 ms

App size

Revision	Plain	With Sentry	Diff
56d9dcc+dirty	2.92 MiB	3.46 MiB	557.25 KiB

[github-actions]

Android (new) Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	367.77 ms	409.09 ms	41.32 ms
Size	7.15 MiB	8.20 MiB	1.06 MiB

Previous results on branch: kw-fix-deprecations

Startup times

Revision	Plain	With Sentry	Diff
56d9dcc+dirty	340.87 ms	374.77 ms	33.90 ms

App size

Revision	Plain	With Sentry	Diff
56d9dcc+dirty	7.15 MiB	8.18 MiB	1.03 MiB