Welcome to Atlassian Community!
I'm not sure if I understood correctly, but you are not able to delete projects, is that correct?
After you click to delete the project, does it show an error or the project is just not deleted? What happens after you try to delete it?
If it shows an error, please share it with us.
I see that you are a site-admin, but to delete projects you must also be in the group Administrators.
Just to let you know the difference, site-admins can manage users and all other settings on Administration's page. The Administrators (part of group administrators) can manage the Jira settings.
So, as you are a site-admin, please go to your profile and make sure you are in the group "administrators" and then, go to the project you need to delete and click on Project settings > People > Add you as administrator and then click on Delete project.
If when you go to the project you only see that page of the screenshot, please, click on "Back to project" and you will see the option "Project settings".
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