If you find that Windows 11 is trying to download and install updates, but keeps on failing, it's probably because they've already been installed, but a bug in Windows is failing to recognise this.
I managed to fix this problem by going into "system" - "troubleshoot" - "other trouble–shooters". From there you can choose Windows update and run a diagnostic test to see if any errors are present. This may take anywhere from 30 seconds to 5+ minutes. If problems are found, Windows may ask you if you want to fix the problem.