I also own an iMac 27'' Late 2013 and I solved the slowness problems by deciding to eliminate the Fusion Drive, open the iMac and replace the mechanical Hard Disk with a 2TB Crucial MX500 SSD.
Now the iMac flies, turns on and login in a matter of seconds and has never gone so well from Maverick to Catalina! 🙂
Keep in mind that with Micropatcher 0.51 I had first installed Big Sur 11.0.1 on the externally connected SSD and it then worked immediately as soon as I replaced the internal Hard Disk and turned the iMac back on.
Now that the 128GB Apple SSD belonging to the Fusion Drive is indipendent (note: I called it Macintosh SD 😉), I have run some Benchmark and in fact Apple has done well to exclude these iMacs 14,2 from Big Sur, due to the numerous models purchased with Fusion Drive. In fact, the read of Apple internal 128GB SSD is 700MB/sec and the Write 300MB/sec. That's fine as long as the Data does not exceed 128GB; after that, since the Fusion Drive does nothing but move the most used data from the HD to the SSD, everything slows down, ESPECIALLY the Parallels Desktop or the VMWare Fusion Virtual Machines.
Now, however, especially since I put the Parallels Desktop VM with Windows 10 Pro in the Apple internal SSD 128GB, Winzozz startup almost instantaneous while before it took minutes as the Fusion Drive wasted time transferring 25GB of VM to the SSD but NEEDING TO FREE THE SPACE FIRST...
The SSDs and the PCI-Nvme Controller used by iMacs from 2015 onwards, on the other hand, are much more performing.