Update form-schema required key information

[MagnusHJensen]

Why:

Closes #23524 To fix missing information that is not present in the docs, but present in the in-file form schema editor:

What's being changed (if available, include any code snippets, screenshots, or gifs):

Adds the Only for public repositories text on each required key.

To align with the github in-file editor documentation:

Check off the following:

• [ ] I have reviewed my changes in staging (look for the "Automatically generated comment" and click the links in the "Preview" column to view your latest changes).
• [x] For content changes, I have completed the self-review checklist.

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[cmwilson21]

@MagnusHJensen Thank you for opening a PR and linking it to your issue! ✨

We appreciate all the screenshots 🤩

I'll get this triaged for review! :zap:

[github-actions[bot]]

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