Hi,
I set CB registration to require admin approval but did not get any admin 'action required' emails. I spent quite some time searching for a solution and trying different things as suggested by the many people who seem to have had a similar problem over the years, including email settings and registration set up options etc
In the end I found a solution that I had not previously seen so thought I would post it for the record.
When I first set up the site I installed everything (Joomla 3.9, CB 2.4). I then added a whole bunch of fields to the registration form, some of them required. I tested the registration process and found the error mentioned (ie no admin emails being sent)
In CB users I had the test account and the Super User account. I checked that the Super User account was set to receive moderator emails so that wasn't the problem. I noticed though that all the user fields I had added were blank in the Super User account because I had added them later, obviously. I decided to try turning off and turning on again the 'receive moderator' emails setting (you never know....) but found when I tried to save the setting it failed because all the required fields were red. I then completed all the blank fields, saved, tried again with another test registration and bingo! I received the 'action required' email.
I have no hard evidence that not having a complete admin profile is what caused the problem but, if like me, you have been scratching your head over this problem, it is something else to try, and it worked for me. Good luck