Um... that's not a bug. You can delete any backup profile EXCEPT profile #1 (the default backup profile). Which profile is currently active (=selected) is immaterial. It's of course not prudent to delete the active profile but you were never forbidden from doing that.
If you do delete the active profile then of course Akeeba Backup crashes because you've told it to look for a profile that doesn't exist. If you log out and then back in from your site's back-end, e.g. by deleting the Joomla! login cookie, this conditions resets and the default backup profile is selected instead.
As for why you couldn't access your site's administrator, it's because you have published the backup notification plugin which also tries to load the (no longer existing) backup profile. You can of course visit another page like /administrator/index.php?option=com_admin and use the icon at the top right corner of the site to log out of the back-end.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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