I upgraded my six-year-old Mac [Macmini6,2 i7 15GB RAM] to Catalina 10.15.6 (latest) from Mojave in August 2020. It’s a long story…
TL;DR - Catalina runs acceptably after some struggle and patience.
Motivation
I use the RAW Power app to edit raw photo data from within Photos. If you do this, you have to do all your editing in RAW Power to keep Photos from using only the jpeg result. If you want to export your edited photo and use the full data values for compression to external format, e.g., jpeg for email, you must export from RAW Power.
(I set up a Keyboard Maestro macro to start up RAW Power from within Photos to make it less likely I forget to do it properly. Photos gives you an option to do it the wrong way.)
After the mid-July security update for Mojave 10.14.6 (2020-04), Photos consistently crashed upon attempting to export from RAW Power. Nik at RAW Power confirmed for me that it was a bug in Mojave/Photos and sent a report to Apple. Nik informed me that RAW Power does work properly in Catalina. A big Thank You, Nik!
Installation
I saw the Big Sur list of supported Macs and my Mac mini [2012 design, purchased in 2014] is not on the list. It seems that Catalina is the last macos version it will run. So after some dithering, and making three CCC backup clones, I upgraded to Catalina.
The Catalina download and installation of the upgrade were successful. There were two or three restarts. The internal SSD was repartitioned into System and Data partitions as expected. That took a long, long time for my half-full 2TB SSD. (I did not time it, but it was more than a couple hours as I recall.) After installation, I checked System Preferences and changed them, where necessary, to my liking.
The Mac ran, but the fan ramped up frequently - every 20 seconds or so. I use iStat Menus to configure my fan to start up as soon as the temperature starts to go up, rather than waiting for overheating, which seems to be the macos default behavior. The temperature didn’t get high, but it would go over 75 C, the fan would ramp up for 20 seconds or so, and then quiet down again.
Sometimes there were pauses of several seconds when changing applications in the app switcher (⌘-Tab).
Looking at Activity Monitor showed a variety of active processes on the top of the CPU list at different times. Among them were WindowServer, kernel_task, media-indexer, photoanlysisd, Desktop Picture (System Preferences), suggestd. CPU utilization correlated with fan ramp up, but only got up to 40% or so on a single core. Memory was about half-utilized.
Anomalies:
- Opening a new window in Finder (⌘-n) showed an anomaly. The new window would have its menu bar up underneath the system menu bar, so the Finder window menu bar was not visible!
- Some of the trackball buttons did not work anymore, so I looked for an update to my trackball driver (KensingtonWorks). Downloaded a new version (which asked for scary permission to “monitor keystrokes”).
- Keyboard Maestro did not work any more.
Installing the new trackball driver and re-booting fixed all of these issues.
The fan kept running frequently. I rebooted again. No change. Things continued thiw way for the next couple of weeks.
Things I tried:
- Reducing the number of open apps. Slight improvement, but the behavior continued.
- Changing the Desktop Picture to a default Catalina picture on both screens, hoping that would reduce the load. It did not. More puzzling, after wake from sleep, or even reboot, the Desktop picture on one of my screens sometimes reverted to a photo I had used in Mojave. I changed it back to the default Catalina picture multiple times.
A couple days ago it occurred to me to reset the SMC and NVRAM. That seems to have made the desktop picture stable. The fan still ran frequently.
The Desktop Picture (System Preferences) ia visible in Activity Monitor, but it is no longer active. However, it has 631.8 MB real memory in use!
Finally, today the fan stopped running! What changed?
Maybe the indexing, or whatever was happening, has come to an end.
All is quiet except when doing something that uses CPU.
Seems OK now! 
