Just tested the Instagram deletion process as of today: you need to use the official Instagram Account Deletion page in a web browser—Instagram does not let you permanently delete your account directly from within the app. Log in, select your reason for deletion, re-enter your password, and confirm—the account is scheduled for deletion after 30 days. No additional tools are required.
Also, for anyone looking to view Instagram content anonymously or save media before deleting their account, Picnob is still the best solution for Stories, Highlights, and even viewing private profiles as of today.