chore(tanstackstart-react): Export custom inits from tanstackstart-react

[github-actions]

Note

The pull request "chore(tanstackstart-react): Export custom inits from tanstackstart-react" was created by @nicohrubec but did not reference an issue. Therefore this issue was created for better visibility in external tools like Linear.

Export custom inits to send correct metadata with data sent from the SDK.

Closes #18366

[linear]

JS-1239

[andreiborza]

#18366