Your big problem is you only have about 2.43GB of Free storage space as of the picture of Disk Utility First Aid. With the macOS Extended file system bad things happen when it runs out of Free storage space.....it can corrupt the files on the drive and other problems. It is also interesting that the First Aid portion you pictured, shows it resizing the Core Storage Logic Volume......that is bad and indicates a bigger problem with this volume/drive.
Try running First Aid on the Fusion Drive item.
I wonder if the Hard Drive portion of the Fusion Drive is failing.
See if you can create a new macOS admin user account using these instructions:
If you don't have another macOS admin user account, then you will need to trick macOS into running Setup Assistant again. This will involve using the command line. These particular instructions will only work on macOS up until about macOS 10.14 Mojave....different instructions are needed for macOS 10.15 to 13.x.....it is impossible to do this with macOS 14.x+.
You can do this by booting into Single User Mode by holding the Command + S keys just after powering on the computer & hearing the startup chime (hold it immediately after the chime...it may not work holding it sooner). Then at the command prompt enter the following commands making sure to press the "Return" key at the end of each line to execute each command:
fsck -fy
mount -uw /
rm -i /var/db/.AppleSetupDone
reboot
If all these commands complete without any errors when you reboot the computer Setup Assistant should run where you can create a new admin user account. Report back here afterwards before doing anything else.
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If you can at least boot into macOS with an admin user account, then we have some more options available to attempt to understand what is happening here.
Do you have a good backup of this system? If not, then you that is a high priority. The easiest method may be to install a full version of macOS onto an external USB3 SSD & booting from that external drive. This would make it easier to backup of the data if needed and to try to troubleshoot a few things as well. It also gives you the option to perform a clean install. If the internal Hard Drive portion of the Fusion Drive is failing, then you will need to boot from an external USB3 SSD if you want to continue using this iMac anyway.