Hello JeffDAM**,**
Good day! Thank you for reaching out to Microsoft community.
The deprecation, which is mentioned this article, is not for business users.
Modern Authentication Methods now needed to continue syncing Outlook Email in non-Microsoft email apps - Microsoft Support.

For business users, to Allow users to create app passwords:
By default, users can't create app passwords. The app passwords feature must be enabled before users can use them. To give users the ability to create app passwords, admin needs to complete the following steps:
- Sign in to the Microsoft Entra admin center as at least an Authentication Policy Administrator.
- Browse to Conditional Access > Named locations.
- Click on "Configure MFA trusted IPs" in the bar across the top of the Conditional Access | Named Locations window.
- On the Multifactor authentication page, select the Allow users to create app passwords to sign in to non-browser apps option.
For your reference: Configure app passwords for Microsoft Entra multifactor authentication - Microsoft Entra ID | Microsoft Learn.

Please note that:
- App passwords don't work for accounts that are required to use modern authentication.
- App passwords don't work in hybrid environments where clients communicate with both on-premises and cloud auto-discover endpoints. Domain passwords are required to authenticate on-premises. App passwords are required to authenticate with the cloud.
- When you disable the ability for users to create app passwords, existing app passwords continue to work. However, users can't manage or delete those existing app passwords once you disable this ability.
- When you disable the ability to create app passwords, it's also recommended to create a Conditional Access policy to disable the use of legacy authentication. This approach prevents existing app passwords from working and forces the use of modern authentication methods.
However, there is another specific channel for your mentioned concern where you will get some possible information for certain specific resources and platform from our related community members.
I understand your concern but since your problem is related to Microsoft Entra, I would also like to suggest you post your concern in the related community i.e., Ask a question - **** Microsoft Entra ID - Microsoft Q&A to get the detailed help from the experts.
[Note: A Microsoft Entra identity service that provides identity management and access control capabilities. Replaces Azure Active Directory].
For more information, you may also check this MS article: Microsoft Authenticator FAQs - Microsoft Support.
Apologies for redirecting you to different community as the members in the category posted focus on the users with out of the box concerns on Microsoft 365 and have limited knowledge on the Microsoft Entra; so, to get the fast and better assistance, we have redirected you in the correct path.
I hope this helps. Let me know if you have any further questions or concerns.
Appreciate your patience and understanding. Have a great day!!
Best Regards,
S M Nazmun Nur