Hello Mimisn,
Welcome to the Microsoft Support Community!
We apologize for any issues you are experiencing with Loop does not show any of the # of mentions when someone mentions you. We will help you solve this problem.
To fix this issue, follow these steps:
Check Notifications Settings:
Ensure that you have enabled notifications for Loop in their device settings. This is crucial for receiving alerts when mentioned in a Loop document.
Adjust Outlook Notifications:
Go to Outlook Preferences > Notifications > Loop and uncheck the option for notifications when mentioned. Restart Outlook and check the option again. This can help resolve issues with missing notifications
Clear app cache: if you are using Loop app
By design, using the @mention on the SharePoint Online sites does not show whether users have permissions and what permissions they have.

In my test, when I share documents with user, the message "Grant Access-Share and notify" will appear.
The specific operation is shown in the screenshots below:


If this is the situation, it means that the user has permissions to this document.
Thank you for contacting a Microsoft Community Support specialist.
Best regards,
Shelby_7891 | Microsoft Community Support Specialist