You can still use Akeeba Backup Professional. You cannot disable update notifications; update notifications are actually generated by Joomla!, not Akeeba Backup. The Download ID is only used when you try to install an update. You can always unpublish the update site for Akeeba Backup from Manage, Extensions, Update Sites. The next time you check for extensions updates Joomla will not look for updates for Akeeba Backup, therefore it will stop notifying you.
Please bear in mind that older versions of Akeeba Backup will NOT work reliably -or at all- with newer versions of Joomla since Joomla! is changing several of its APIs all the time. It will most definitely not work with Joomla 4, scheduled for release this summer. Also bear in mind that newer versions of PHP and MySQL are only supported in newer versions of Akeeba Backup. While this seems to be irrelevant when you are stuck on an old server it becomes very relevant when you try to restore that backup on a local server and suddenly find out that it's no longer possible or, worse, that happens when going from your local server back to the live server.
Finally, I would also like to note that the Essentials package which includes both Akeeba Backup and Admin Tools is 60 Euros (instead of 80) for the first year and 42 (instead of 56) for every next year. That comes down to an extra €1,17 per month to have reliable backups. That's about the price of an espresso in Denmark :)
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!