To use Assistant in the Safari browser you need to open the Safari extensions settings and enable this checkbox.
The browser will ask you for access to activate the extension, then click Turn ON and the extension starts working.
I have the same problem. Is it really necessary to re-boot in Safe Mode?
App Store had AdGuard extension, and I "got" it.
I saw the Safari preferences "Extensions" populate properly.
Tried to follow the instructions from AdGuard to click on the checkboxes, but Safari rejected all clicks. Message is:
Safari detected an app or service that interfered with clicking. To protect your privacy and security, this extension was not turned on. After quitting the app or service, you can try to turn on this extension again. (Learn More....)
"Learn More..." had this text:
If you can’t turn on extensions in Safari
Learn what to do if you can't select the tickbox to turn on a Safari extension.
macOS Catalina introduced a security feature designed to prevent malicious software from tricking you into turning on a Safari extension. In some cases, this feature can be affected by the use of legitimate software that has certain screen-recording or accessibility features. If that happens:
You might see a message stating that Safari has detected an app or service interfering with clicking.
You might be unable to turn on Safari extensions in Safari preferences. You can deselect a tickbox to turn off an extension, but you can't select a tickbox to turn it on.
Install the latest Apple software updates, then try again. If you still can't turn on Safari extensions, start your Mac in safe mode by pressing and holding the Shift key as your Mac starts up. Turn on any Safari extensions that you want to use, then restart your Mac normally.
I'm running macOS Catalina 10.15.7 and Safari 14.0.3