Thanks to the community we could now find the problem why RUI3 BSP installation fails in ArduinoIDE V2.x.x
The problem is the file name of the JSON file.
In ArduinoIDE V1.x.x this URL works without problems: package_rakwireless.com_rui_index.json. But in ArduinoIDE V2.x.x it fails due to a problem to parse the URL correct. Reason seems to be that there are two dots in the filename.
From now on, please use the following BSP URL:
https://raw.githubusercontent.com/RAKWireless/RAKwireless-Arduino-BSP-Index/main/package_rakwireless_com_rui_index.json
We will keep both file versions for some time, but the old filename will disappear with the next release.