Many thanks. GPU History shows nothing happening i.e. no bars showing.
I have to admit, I've patched this old iMac to run Catalina. One of the patches installed is called "Legacy Video Card Patch". I've used that patch because my GPU is an old non-metal Radeon HD4850. So, if Activity Monitor is looking for "metal" activity, it will find none.
I've also tried iStatMenus which provide a separate chart of GPU memory used and GPU processor activity. Memory is being used – sometimes more than 50% but processor activity showing is zero. That reinforces your thought that macOS is looking for a metal capable GPU.
The iMac is quite slow. Geekbench reports it is 50% the speed of comparable iMacs. Geekbench have quite a lot of saved bench tests for the same iMac running 10.15.7. Most of those reports are twice as fast as my iMac. I had an SSD installed a few years ago and recently added RAM. It's now running 16GB. The memory upgrade didn't improve the speed. I've been trying to find out why it is so slow. I thought the patching might be a factor so, I downgraded to 10.13 thus removing all the patches. It was perhaps 2% quicker.
Apple Hardware Test found no problems (except for missing HDD sensor). It's very hard to find software that can look at such an old GPU and CPU. Geekbench5 can't. Intel's Power Gadget can't look at the old CPU (Core i5-750). So, it's very hard to diagnose for issues.
Anyway, thanks for the ideas.