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Hi Akshay,
When we create a new team site connected to Microsoft 365 group, members and owners added to the Microsoft 365 group associated with the site are automatically added to the site owners and members group. You could refer to this article for more information.
If you check the modern SharePoint team site interface, it shows both the owners and members of the Microsoft 365 group and when you check Settings>Site Permissions, it shows the group name, you might not see the names of the users. Under Site owners and Site members, only groups—not people—are displayed.
Now when you go to Advanced permissions settings and click Site owners and Site members, you will again see the group name and not the user. This is because the owners we specified during the creation of the SharePoint team site were only added to the Microsoft 365 group.
M365 group and SharePoint group have the same name, I understand this can make the users confused but they are not same. Please read the article below, it has the explanation in detail.
Groups permissions vs. SharePoint permissions
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In your second screenshot, I understand site owner group is not visible, this is because by default, the Site Owners group is hidden in the list. To make it appear, please follow the steps in the screenshot below.
If you need any help, please let me know.
Regards,
Neha