Hi, @LM-5132
Thank you for posting your question in the Microsoft Q&A forum.
According to your description, you have encountered the problem that the encryption option in Outlook is not available.
First of all, regarding the problem of no encryption option in OWA. You can first use Exchange Online PowerShell to verify whether the tenant is correctly configured for Microsoft Purview Message Encryption. Use the command to check whether the Information Rights Management (IRM) feature is enabled in Outlook Web Edition.
Get-OwaMailboxPolicy | FL *IRMEnabled*
Regarding your second question, it is not possible to send encrypted emails from the work Outlook desktop. I agree with @Andy David - MVP's answer that your organization needs to obtain permission and enable the feature. The only prerequisite for using Microsoft Purview Message Encryption is that Azure Rights Management must be activated in the organization's tenant.
Regarding the question of whether you should use the encryption option S/MIME or set up public/private keys, S/MIME is a widely accepted method for sending digitally signed and encrypted messages. You can also choose to use various encryption technologies together.
Refer to: Resolve Microsoft Purview Message Encryption issues - Microsoft 365 | Microsoft Learn
Set up Microsoft Purview Message Encryption | Microsoft Learn
Best,
Jeanne