Based on your description, I would like to further confirm your question.
1.Do you want to realize that users can log in to OWA but will not be presented with the login screen?
2.What do you mean by “present a different page”? Are you referring to customizing the OWA login page?
Based on my personal experience, if you want OWA to log into the mailbox but not show the login page, it usually means you want to implement SSO.
You can configure ADFS to automatically log in when accessing OWA. For more information, please check How to setup Microsoft Active Directory Federation Services [AD FS] - Virtually Boring
If you want customize the OWA login page, please check Customize the Outlook on the web sign-in, language selection, and error pages in Exchange Server | Microsoft Learn
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