Blocking Personal Outlook and Gmail Accounts on Corporate Device

In Entra, you use the Web Content filtering policy (see below) > You will need to create a new policy (my demo account does not have it) this is the guide: https://learn.microsoft.com/en-us/entra/global-secure-access/how-to-configure-web-content-filtering

Then you can add the domains that you'd like to block within the rules.

For Microsoft Purview, it's more of blocking sensitive data from being uploaded/ used in specific cloud domains, think of it as an extra measure to ensure that your users will not be able to upload to Hotmail or Gmail. https://learn.microsoft.com/en-us/purview/endpoint-dlp-using?tabs=purview#scenario-3-modify-the-existing-policy-block-the-action-with-allow-override