docs(new-release): Update docs based on new Craft flow

[github-actions]

Note

The pull request "docs(new-release): Update docs based on new Craft flow" was created by @s1gr1d but did not reference an issue. Therefore this issue was created for better visibility in external tools like Linear.

We don't need to create PRs to add new packages to the registry. Craft can now do this automatically.

Documented here: https://craft.sentry.dev/targets/registry/#creating-new-packages

[linear-code]

JS-1908

[github-actions]

A PR closing this issue has just been released 🚀

This issue was referenced by PR #19731, which was included in the 10.44.0 release.