I'm not sure why your iCloud account would stop working on old devices. I can still log into devices with Mac OS 10.11 with my iCloud account. Maybe because MFA was introduced a few years ago?
But like the previous comment said you can use OCLP to install new versions of MacOS on "unsupported hardware". Usually you can go 2-3 versions of newer MacOS without any issue. Beyond that little things will start breaking, but it will still be functional.
I run the newest versions of Sonoma on a 2010 iMac (that I upgraded to a quad core CPU, Metal capable GPU, and 32GB of RAM), a 2012 Mac Pro 5,1 (also upgraded to dual 3.46GHZ CPUs, RX 580, and 64GB RAM), and a 2009 MacBook Pro (SSD, and RAM Upgraded).
At some point security updates to iCloud logins break older systems. They don't intentionally break it when an OS goes out of support, but they don't fix it anymore, either.
There are versions of iOS on iPhone that can't do iCloud-stuff anymore.
Generally because the versions of SSL/TLS are outdated on those devices and so either need modern cryptographic libraries installed on them or they just cannot connect to ansy modern server.
I can either use the apple account on the latest iOS or on the old Mac mini but not on both. Basically when I’ve tried to log in on the iPhone it told me I need to upgrade the Mac mini or remove it if I want to use the account on my iPhone. Obviously I removed the account from Mac mini. Perhaps I can create new account specifically for Mac mini but what’s the point to have different iCloud iMac accounts for each device? I’m confident but at some point this trick will stop working as well.
But like the previous comment said you can use OCLP to install new versions of MacOS on "unsupported hardware". Usually you can go 2-3 versions of newer MacOS without any issue. Beyond that little things will start breaking, but it will still be functional.
I run the newest versions of Sonoma on a 2010 iMac (that I upgraded to a quad core CPU, Metal capable GPU, and 32GB of RAM), a 2012 Mac Pro 5,1 (also upgraded to dual 3.46GHZ CPUs, RX 580, and 64GB RAM), and a 2009 MacBook Pro (SSD, and RAM Upgraded).