Please read again what you pasted. The time is actually correct.
The first date and time is in timezone CET (Central European Time).
The second date and time is in timezone GMT+00:00 (Greenwich Mean Time).
When it's 14:50:56 at GMT it is 15:50:56 at CET (GMT+01:00).
Therefore the stored and displayed date and time is correct. What you want is to display that time in a different timezone. That's very different than the time and date being wrong :)
The timezone used for listing backup archives is the timezone of your site as set in System, Global Configuration, Server, Website Time Zone unless you have overridden it in your user profile (User Menu, Edit Account, Basic Settings, Time Zone). So, go to User Menu, Edit Account, Basic Settings, and set the Time Zone to Berlin. You will now see that Akeeba Backup lists the backups in your timezone, CET (Central European Time, which is the Berlin time zone).
Finally, keep in mind that the date and time in the backup description (the underlined part in “ Backup taken on Samstag, 07. Januar 2023 15:50 CET ”) is static text. It is generated by Akeeba Backup based on your site's timezone (System, Global Configuration, Server, Website Time Zone) and the site's language at backup time. It will not change when you change the timezone settings of your site or user account.
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!