Sharing this information for those that cannot open existing ArcGIS Pro projects in ArcGIS Pro 3.0, and it may be due to a standalone table connection issue.
If your project points to an Excel datasheet or CSV file or other standalone data connection, the project may not open unless you update to the latest 2016 Access Database driver. https://www.microsoft.com/en-us/download/details.aspx?id=54920
However, when attempting to install the 2016 Access driver you may find yourself in this situation where Windows will not allow you to install either the 64 bit version or 32 bit version (see link below).
C:\Users\myuser\Downloads>AccessDatabaseEngine_X64.exe /quiet
I've had this issue and also wanted to throw out a suggestion that's worked for me. I occasionally have to reinstall the 2016 driver and restart my computer when existing projects don't open. It usually works after that. (ArcGIS Pro 3.0.2)