Rescue Mode only works when your IP is temporarily blocked. It does not work when you have set up an Administrator Exclusive Allow IP List (IP whitelist to access the administrator) which does not have your IP in it.
Read https://www.akeeba.com/documentation/admin-tools-joomla/atwafissues.html under "Using FTP to regain access to your site's administrator" and "Administrator Exclusive Allow IP List". It tells you which file to rename to (temporarily) disable Admin Tools so you can regain access to your site. You can then change your Allow IP List with your new IP, and rename the file back to restore protection to your site.
I generally recommend against using the Administrator Exclusive Allow IP List when you have a dynamic IP address. Sure, your host may be trading it as mostly static but, as you saw, if there's a power outage or any other network disconnection it will be cycled. ISPs will also do that when their side of the network gets upgraded.
The documentation has a workaround for that. Set up a dynamic DNS – there's a fantastic German company I use for this: INWX. Let's say that you set up dynamic DNS for the subdomain an.example.com. Add @an.example.com and #an.example.com into your Administrator Exclusive Allow IP List. This tells Admin Tools to resolve your subdomain (an.example.com) to an IPv4 (@) or IPv6 (#). If your IP matches the resolved IP of your domain it's allowed. Since the dynamic DNS domains have a very low TTL (Time To Live) between 120 and 300 seconds, any change in your IP address will be reflected within a few minutes and let you access your site without having to rename files over (S)FTP. It will cost you a few Euro per year to get a domain, and spend a few minutes once to set up your router or NAS for dynamic DNS. Seeing you're German, you are likely to be using Deutsche Telekom's Fritz!Box router or a Synology NAS which I can tell you from personal experience both support dynamic DNS. If you're wondering, my ISP in Greece is owned by DT (and recently renamed to Telekom); I use the same router. As for the NAS, I bought a Synology NAS because Germany is my second largest market and it looks like y'all are using Synology NAS; I can see why, it's pretty neat.
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!