Hi @IBN
It's a safe bet to try deleting the public site as you have 93 days to restore the SharePoint Site if this has caused any issues. If they have separate SharePoint URLs then they are not the same SharePoint site.
Restore deleted sites (If you run into issues)
https://learn.microsoft.com/en-us/sharepoint/restore-deleted-site-collection
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If this is helpful please accept answer.