The original Catalina disk ended up getting the Apple/Update folder in the EFI as well. I actually cloned the Catalina NVME drive to an SSD, and that's where I installed Big Sur. I typically always perform the update/install on a clone drive so I don't currupt the main drive I use if the install goes bad. The ssd drive that I installed BigSur had no EFI on it. After the install, the Big Sur ssd had an EFI folder with only an Apple/Update folder tree. The main nvme drive I still have Catalina on, still had its original EFI folder, but with the Apple/Update folder added to it.
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