In addition to the post above, I suggest you try using Monterey or Big Sur with that older Mac Mini. I don't have it now, but I did have a MBP8,2 from 2011 that ran much better on Big Sur. It was a problem because those MBP had Radeon GPUs that were prone to sudden death. That particular machine lasted years, but I disabled the discrete GPU using a terminal nvram command. The machine ran hotter than normal but it was usable. Not so with Ventura, which does require a lot of root patches! Of course, going back to Big Sur is a lot of hassle, but it may be worth the time.
I actually think those non-metal computers should be put out of service when that is possible, and now that you have that good iMac, maybe the Mac Mini needs a rest, or at least use as a music server or the like.