In reply to Graeme G:
Worth running Onyx for your version of OSX - I doubt that it will fix things, but there's a small chance, and it is free and safe.
Ultimately I agree with the SSD idea. You have a couple of options. Putting in an SSD: I have done this on 27", 24" and 21.5" iMacs and it isn't that hard. Clear away all children, dogs, flies etc and put aside an hour of concentration. The screen coming off is usually fairly easy (many of the models are held on by magnets and pull up with a pair of small window suckers like glaziers use, the others are easily sliced through and the glue/foam can be removed afterwards). I'd suggest going to everymac.com to check your model and see what the max RAM capacity actually is and the model number, and then go to iFixit.com to get really good walkthroughs (still and video) of how hard or easy it might be. For instance, most 2015 iMacs can use up to 32Gb RAM so you could easily double your 8Gb (which is probably two 4Gb sticks behind a little door that just unscrews). Have a look at your model and decide if you are up to it... there are good little sets made by OWC that contain all the things you need including slicing tools to get the stuck on screens off, suckers, thermal cables and sensors for the new drive etc.
Alternatively, sod all that for a laugh and just buy an external SSD hard drive. Plug in, format using the Disk Utility in MacOS, and then install Big Sur on it. Then go to Preferences >Start Up>choose the external SSD. This is the cheapest and safest (non-destructive) way to do it and if you are nervous of opening up an iMac and fiddling is incredibly easy, and pretty effective. Due to the bottleneck of USB in 2015 compared to the internal connectors it will be a bit slower than an internal SSD, but still very much better than what you currently have, as well as much cheaper than paying someone to do it. Don't buy an external spinning HDD, it has to be an SSD. It doesn't need to be big - 256Gb or 512Gb would be fine - you can keep all your data on the internal spinning drive and just run the OS from the SSD if you want. Having said that a 1Tb external USB bus powered SSD looks to be less than a hundred notes on Amazon. Just don't unplug it or you will be back to square one wondering why your machine has gone so slow again as it defaults back to the internal HDD.
Ultimately, the Intel Macs will probably lose support in a couple of years, ahead of which it might be wise to flick it on while it still has some resale value, and buy an Apple Silicon model. So sorting out a useable machine for another 12-18 months is more sensible than a potentially expensive third party upgrade. I would wait until the next iMac release comes out though, as the current model is a single size and may be smaller than you want and the chipset is about 18 moths old (although still blisteringly fast compared to Intel models); the M2 model is widely expected to be released later this year.
HTH
b