Norton 360 stopped launching soon after Big Sur 11.4 installation

Consider yourself lucky. First, there is no reason to ever install or run any 3rd party "cleaning", "optimizing", "speed-up", anti-virus, VPN or security apps on your Mac.  This user tip describes what you need to know and do in order to protect your Mac: Effective defenses against malware and other threats - Apple Community.  

There are no known viruses, i.e. self propagating, for Macs.  There are, however, adware and malware which require the user to install although unwittingly most of the time thru sneaky links, etc.   

Anti Virus developers try to group all types as viruses into their ad campaigns of fear.  They do a poor job of the detecting and isolating the adware and malware.  Since there are no viruses these apps use up a lot of system resources searching for what is non-existent and adversely affect system and app performance.

There is one app, Malwarebytes, which was developed by a long time contributor to these forums and a highly respected member of the computer security community, that is desshoigned solely to seek out adware and known malware and remove it.  The free version is more than adequate for most users.  

Also, unless you're using a true VPN tunnel, such as between you and your employer's or bank's servers, they are useless from a privacy standpoint: Public VPN's are anything but private.  

So uninstall the Norton software according to the developer's instructions.

There are no known Viruses in the wild that self replicate and affect macOS. There are Malware and Adware that does affect macOS and are often times downloaded as part of an Application from Third Party UnTrusted Site and get installed along with the Application.

Suggest downloading from a Trusted Developer and Respected ASC Contributor the application Malwarebytes for Mac. It is free or paid for added features. Run the Application and it should remove the malware / adware. Once done, restart computer and test.

Any Third Party Applications that will interfere with the normal operation of the OS, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS. Norton 360 falls into their category

Consider this a sign from God...

Remove Norton 360 from your Mac entirely. It's completely worthless on a Mac and nothing but a waste of resources.

Welcome and thank you too :-)