Hi Victor,
Thank you for posting back and sharing these detailed information with us.
It looks like only a specific SharePoint site doesn't have "Site information" in Settings. And your coworker has a SharePoint site having the same situation.
I double check the SharePoint sites link you provided, it's a bit different from SharePoint team site I create from SharePoint home page > Create site > choose "Team site".
The link you provide is like https://***.sharepoint.com/teams/sitename
While when I create SharePoint team site in SharePoint home page, the link is like
https://***.sharepoint.com/sites/sitename
I tested further and found I can create SharePoint site with the similar link as yours from SharePoint Admin Center>Active Site>Create>Other Options>Choose a template from More templates>then I can choose teams template.
After that, when I opened the created team site, I found I cannot delete site from Settings>Site Information, because there is no "Delete site" option.
It looks like this kind of team site cannot be deleted by using the path Settings>Site Information>Delete site.
In this situation, I recommend you try following ways and see if you can delete the SharePoint site:
1.Access Site Settings page by using the following link:
https://***.sharepoint.com/teams/sitename/_layouts/15/settings.aspx
Note: please adjust the link to apply to the situation on your side.
Then check if you can see Delete this site in Site Actions, as shown below

2.If you don't have Delete this site option on this page, you may try following link to access the delete site page: https://***.sharepoint.com/teams/sitename/_layouts/15/deleteweb.aspx
Note: please adjust the link to apply to the situation on your side.

However, if you still cannot delete the SharePoint site, since only a specific SharePoint site has the issue and you just need to delete the site, I would recommend you try to contact your Microsoft 365 global admin or SharePoint admin, they have permission to help you delete the site from SharePoint Admin Center.
Appreciate your understanding and cooperation.
If you have any questions about the 2 links I mentioned above, you can post back and I will help you.
We hope you have a nice day and stay safe!
Sincerely,
Tina | Microsoft Community Moderator