I would like users to only be able to delete their own files, But edit and view everything else.
Is this possible in SharePoint Online?
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Yes, it is possible. You could use workflow to set item level permission.
1.Create a custom permission level exclude "delete items".
Note: To add the Impersonation Step, you need to give workflow app permissions: https://docs.microsoft.com/en-us/sharepoint/dev/general-development/create-a-workflow-with-elevated-permissions-by-using-the-sharepoint-workflo