The 1603/1605 errors we see there are typically a previous other installation stuck, or a problem in the Windows update/install processes.
If you see msiexec running in Task manager-processes, kill it and try this launcher install again please.
Otherwise run the Update app in Windows, does it load okay, find anything to apply - whether a patch, update, or whole new Windows 10 version? If so do that and reboot, then try this launcher install again please.
If still no good, do you see Paradox Launcher v2 in the Windows Control Panel to uninstall? If so does it uninstall cleanly, or get an error doing that? Use this MS tool to remove the stuck install/uninstall:
If you see msiexec running in Task manager-processes, kill it and try this launcher install again please.
Otherwise run the Update app in Windows, does it load okay, find anything to apply - whether a patch, update, or whole new Windows 10 version? If so do that and reboot, then try this launcher install again please.
If still no good, do you see Paradox Launcher v2 in the Windows Control Panel to uninstall? If so does it uninstall cleanly, or get an error doing that? Use this MS tool to remove the stuck install/uninstall: