Late 2013 iMac: help with troubleshooting intermittent crashing problem

Solution 1:

1. Let’s skip Console.app and check the source. Open /Library/Logs/DiagnosticReports and order the contents by descending date. Check for any reports around the time of your crashes. You want to look fro files ending in file extension .panic, .spin or .tailspin. If you find any, please provide a way for us to view those files.
2. I’d suggest scanning your filesystem for corruption (i.e. Disk Utility) though I expect it to turn out OK, given that this issue seems to survive full disk erases.
3. Are there third-party kernel extensions that you have installed? Please provide a copy of the output of the Terminal command kextstat.
4. Can you work for a while in Safe Boot Mode (booting with Shift held down) and see if the problem persists?
5. Do you have any third-party devices attached? Can you run without them?

UPDATE:

1. Can you share the output of pmset -g log for the timespan between your most recent clean boot and the subsequent reboot after failure?
2. Can you try reproducing this issue a few times and see if you consistently see the Chrome wakeups_resource.diag file in your logs around the time of hang? If so, please find a way to share the file (e.g. via PasteBin). Chrome may be indirectly responsible for an interrupt storm and we might be able to see that.
3. After reproducing a few times, can you temporarily stop using Chrome completely and try living on Safari?
4. If the hangs continue without Chrome ever running, can you try uninstalling Virtual Box and DropBox? (Make sure that kextstat doesn’t show them anymore.) Even though you are not running those apps, these kernel extensions start at boot and are always loaded into kernel memory so we have to remove them to eliminate the possibility that they’re involved in the failure sequence.
5. Can you list the filenames of the new logs that appear in DiagnosticReports?

Re: your comment about safe mode:

I will try running safemode for some days and see if these crashes still occur. I understand that will mean it's a hardware issue, but what component/sub-system?

Actually, the overwhelming majority of unstable behavior these days is due to software (and occasionally firmware) bugs. Your symptoms don’t smell like hardware failure, particularly since you’ve tested both your HDD and your DRAM. There is very likely a software cause and fix for this.

Solution 2:

This may not be a definite answer, but since I have a iMac (21.5-inch, Late 2013), I might as well post my observations.

The internal drive on this Mac is a 1 TB HDD. The Mac did not start significantly slowing down until I installed Mojave, This is also where APFS was first used. Upgrading to Catalina did not help much.

There have been posts here at Ask Different which after reading I came to the conclusion that if APFS is employed, then you need a SSD. Being that the Mac can not up upgraded beyond Catalina, I was not really willing to open the Mac. So I pursued adding an external SSD. There is really nothing out there for Thunderbolt that I did not consider prohibitively expensive. USB 3.1 gen 1 (which is USB 3 or 5 Gb/s) SDD drives have come down in price and have type A plugs. (Both the 21.5" and 27" late 2013 iMacs have USB 3 jacks.) I choose an Inland Professional 480GB SSD which cost 55 USD. However, the USB cable was to short, but I already had a longer spare. This significantly improved the performance of my iMac.

I can run Big Sur in a VirtualBox virtual machine with better performance than when I ran Catalina on the internal HDD. (Yes, it does seem odd that you can not run Big Sur on the actually iMac, but you can in a virtual machine without having to perform any special hacks or modifications.)

I have been using the new external SSD for a month and only had one occasion where the problem you described with the fan speeding up followed by the Mac hanging. This was when I was working on a solution to question for Ask Different and Big Sur hung. This caused VirtualBox to hang and eventually the entire iMac. Anyway, the problem was definitely caused by the VirtualBox application.

You say you tried Chrome and Firefox. You might consider Microsoft Edge.

One other concern is there does not seem to be any indication of trim support for the external USB SSD. This may result in the drive eventually slowing down, but so far there is no indication of this happening.

You seem willing to open your Mac and replace the existing fusion drive. I wonder if you could not keep the existing drive and just add a SSD. There is some indication that you could add a secondary SSD "Blade" drive. Being a PCIe connection, this should result in significantly better performance that the existing primary SATA fusion drive. See OWC website for more information and videos.