I have ArcPro 2.9.1 and when starting without a template from the splash screen, Pro takes about 2 to 3 minutes to open the blank project. I would think it should take 10 seconds or so.
If this is a recent event, clear out your caches (display etc)
or have a look at
Troubleshooting Performance Issues in ArcGIS Pro - Esri Community
if it is otherwise
If it's doing this on a blank project, make sure you don't have anything in your Favorites that is set to "add to new projects" that might be slowing it down. Network folders, remote databases, etc.
Maybe also try opening the diagnostic monitor (Ctrl Alt M) and see what tasks are happening in the background.
Another thing to try is renaming your ESRI folder located in the C:\users\user_profile\appdata\local and C:\users\user_profile\appdata\roaming to ESRI_OLD. If this doesn't help, perhaps a full uninstall and clean reinstall of ArcGIS Pro 2.9.0 first before upgrading to ArcGIS Pro 2.9.1
What type of license are you using? Single use/concurrent use or named user?