Please read https://www.akeeba.com/news/1747-joomla-4-is-around-the-corner.html
Also note that the Update Check feature in Joomla is COMPLETELY BROKEN AND THEY WON'T FIX IT. I have reported this four times in the year BEFORE Joomla 4.0 was released. The information it provides is completely inaccurate as the sources of this information were NEVER designed to provide upgrade information!
Yes, Akeeba Backup 8 is not designed to work on Joomla 4.1 or later. However, the upgrade process is upgrade to Joomla 4, install Akeeba Backup 9 and follow the instructions in Akeeba Backup 9 to migrate the settings and backups, then uninstall Akeeba Backup 8. This is not something which can be prescribed in the update XML source which only lists which version of the software is compatible FOR INSTALLATION ON a specific Joomla version. These are two completely different semantics.
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!