Hello, that process usually completes in under 10 seconds on the first start up of a new installation of ArcGIS Pro. At this point you will need to kill the process unfortunately.
In your user profile's Esri Local Caches folder (C:\Users\<user>\AppData\Local\ESRI\Local Caches) you'll likely see a series of g0 and g1 cache files. These are what is generated when the geoprocessing cache is created as you pictured. You might have several of these files if you've used previous versions of ArcGIS Pro. The Pro 2.8 cache files are ~105KB for the g0 file and ~745KB for the g1 file on my machine.
Find the g0/g1 files with a timestamp of today, remove them from the cache directory onto your desktop, make a zip, and upload here please. You can delete all of the g0/g1 files from the cache directory and restart Pro. Try opening the geoprocessing pane to see if cache completion is successful.
We have seen caching fail previously when there is corrupt or out of date Python environment active on your system, perhaps from a previous installed version of Pro.
Let me understand your possible steps based on your screenshot.
- New project
- Insert map
- Add few rasters
- Save project
- Caching hangs?