I just found the solution to this upsetting problem, thus I am sharing the relevant information with the community.
Please comment if you are also experiencing the following issue, and consider informing affected users in relative communities.
Under Windows 10/11, protected by ESET Internet Security (and probably all other ESET products), the default settings for ESET Browser Protection messes up with Firefox installations, as also with the automatic and non-automatic Firefox update mechanism, either when using the background update service or just the temporary background update "service", installed under ProgramData.
When you have enabled ESET Browser Protection for all browsers, it locks Firefox related folders over Windows 10/11 installations, including the profile folders, both for the main installation, under "%AppData%\Mozilla\Firefox\Profiles", as also for all portable installations, under their respective folders, and the background update service folder under ProgramData, namely "%ProgramData%\Mozilla-1de4eec8-1241-4177-a864-e594e8d1fb38", used by both the main installation and all portable installations.
The locking happens the first time you run Firefox after enabling ESET Browser Protection for all browsers, whether it is the main installation or any portable installation, and stays permanent in the system until disabling ESET Browser Protection for all browsers, where all locking information gets flushed immediately.
While Firefox can access these folders, for all other applications, even if Firefox is not running, you cannot access any file inside the locked folders, and if you try to copy or rename any of the files or their parent folders, you get a prompt for administrator permission, then a prompt from your own user account permission, which finally leads to an underlying access denied error.
Under Windows Safe Mode, where ESET does not run in the background, you can access all these files and folders, copy, rename, and delete them, but the frustrating part is that upon restarting in Windows Normal Mode, the above behavior continues, and the even worse part is that any folders being deleted under Windows Safe Mode are somewhat still locked, because if you try to create a New Folder and name it exactly as the deleted one, you get a prompt for administrator permission, then the folder gets created, but it immediately gets locked.
This malfunction heavily affects the update mechanism, for the main installation and any portable installations, causing immediate crashes upon loading, requiring having to restart in Windows Safe Mode, and manually deleting the Mozilla folder under ProgramData, in order to restore normal Firefox operation.
To solve all these issues, you have to disable ESET Browser Protection for all browsers, which is the second option underneath the Enable Safe Banking & Browsing option in the settings.
ESET - Setup - Advanced Setup - Browser Protection - Safe Banking & Browsing - Enable Safe Banking & Browsing - Browser Protection - Secure All Browsers