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Dear Muhanned Shaker,
Thanks for writing back and sharing the requested information with us.
As per the further updates, I have created a test environment with the same regional settings in the SharePoint Online site, where the =TODAY() is producing the correct date but I have tested with the different time zone with UTC+9, UTC+12 etc., where the actual date should be May 9th but the result is still showing May 8.
To my understanding & knowledge, the behavior we are observing with the TODAY() function is not an expected and I believe the problem should be further investigated by the related development team, where they can collect the HAR logs while reproducing the problem and perform the further investigation.
Note: I have checked the service health dashboard at the Microsoft end, where there is no related incident found.
So, I request you to connect with your IT admin of your organization (How do I find my Microsoft 365 admin? - Microsoft Support) and raise a new service request from the Microsoft 365 admin center so that the related development team will connect with you and investigate the issue further.
Reference: Get support - Microsoft 365 admin | Microsoft Learn
Note: We apologize for redirecting you to related development support team because the moderators in this community are limited with the resource for further investigation and to get a quick resolution to your problem, we requested it.
Appreciate your patience and understanding. Have a great day!!
Best Regards,
Sophia