After problematic upgrade to Big Sur, new hard drive in Finder

I don't see any issues with either drive, but the hard drive's Load Cycle Count (attribute #193) is getting to the drive's lifetime maximum value. Most hard drives I encounter with my organization are usually long over the maximum lifetime value.....those drives usually have performance issues and other odd issues, so I will not use them at that point. I've rarely seen hard drives approaching this point so I'm not sure if they will have any performance or odd issues. Something caused your Fusion Drive to become split. Did someone try to perform a clean install of macOS? If so, the clean install was performed incorrectly to maintain the Fusion Drive.

Currently macOS is only installed on the slow internal hard drive. In order to recreate the Fusion Drive, the data on the internal hard drive will be destroyed, so make sure to have a good backup before recreating the Fusion Drive. Here is an Apple article with instructions for recreating the Fusion Drive:

How to fix a split Fusion Drive - Apple Support

What is the exact model of your iMac? You can get this by clicking the Apple menu and selecting "About This Mac", or you can enter the system serial number here:

Check Your Service and Support Coverage - Apple Support

Unfortunately the Software Update in System Preferences/Settings tends to not provide the actual installer options once a newer version of macOS has been released....even if that new version is incompatible with your Mac...it seems to confuse the Software Update functionality. You can find links to many macOS installers in this Apple article (please read it carefully & completely since some installers have a bit of work involved):

How to download and install macOS - Apple Support

Run the following command in the Terminal app so we can get a look at the drive layout (if it is an older OS, then you may need to omit the "internal" part, but make sure to unmount all external drives & images first before using the command without "internal"):

diskutil  list  internal

It appears your iMac had a Fusion Drive which is now split. Usually this means one of the two drives making up the Fusion Drive is bad....usually it will be the hard drive. Right now it appears macOS has been installed onto the hard drive and the "APFS Physical Store disk1s2" is the remnant of the SSD portion of the split Fusion Drive.

Lets check the health of both the internal hard drive and SSD by using DriveDx (free trial period available). Post the complete DriveDx text report here for both of the internal drives using the "Additional Text" icon which looks like a piece of paper.

Running macOS using only the hard drive as you are now means you have slower transfer rates. At best around 70MB/s, but can go as low at 30/40MB/s. With the Fusion Drive, the SSD acts as an intermediary so transfers are typically about 200 to 300MB/s depending on the amount of data being transferred at one time (may be much faster for small transfers 1,500MB/s). I'm guesstimating on the Fusion Drive transfer rates based on my murky memory of reading EtreCheck reports posted on this forum which report the results of a short speed test.

I would recommend turning off "Put hard drives to sleep when possible" in the Energy Saver System Preferences which may help to slow down the rate of the Load Cycle Count increase since your hard drive is getting near the manufacturer's expected lifetime value for this attribute (this attribute is an indicator of how often the drive's read/write heads are fully parked). Of course the hard drive will remain spinning all the time unless you power of the iMac.