I don't think there's anything more I can do without investigating your install. You'll need to PM backend super user login credentials and provide steps to reproduce your issue. I'm not having any problems with privacy consent or MFA in my local testing environments.

Clicking Logout by the User in the Logged In Users logs the user out of the Admin module.

You probably have shared session if frontend logout is logging you out of backend. That's configured in Joomla's global configuration.

Clicking the Login link on the front-end displays the username and a button to "Logout?"

That's just taking you to the login page so that's working as expected.

I meant to voice my consternation and confusion over why the Logout link (restricted to Registered user access) did not work

It does seam strange logouts are not working. That menu item certainly should log them out and typically redirect to homepage.

and also my frustration over the fact that logging the user out from the Admin backend is not reflected in the public front end.

I'm not sure what to do about that. That's Joomla's admin module and we've no control over it. Wonder if something is blocking logouts in general. Maybe 3rd party Joomla User or System plugin as either could interrupt the logout process.

I am also confused as to why the Login does not auto-redirect to the user Profile and that the front-end link to "Your Profile" (restricted to Registered user access and linked to CB Profile module) acts as a dead link (404 Error).

That might just be a problem with the login redirect URL. Do you have a login redirect URL specific in your CB login module? If so please provide what it's set to. Normally it should be non-SEO beginning within index.php. So for example to redirect to CBs profile page you'd use the below.

index.php?option=com_comprofiler

If you want this to use a specific menu item don't forget to add &Itemid to it. Example as follows.

index.php?option=com_comprofiler&Itemid=MENU_ID_HERE

Thanks, Kyle. I'll setup Admin login access for you - I need a valid email address for you to do that.

Use a dummy email address (e.g. testing@cb.invalid). I'll change the email address temporarily if needed for testing emails.

What issues exactly are you wanting me to investigate here? This topic originally was for MFA, but turned into privacy consent, and now logout issues. Please understand I'm not general Joomla support. This is specifically to investigate a potential bug in CB.

You can use an alias email address of your own. Example as follows.

I don't like people using my email address for accounts as I've had far more than I can count just leave the account on the site instead of removing it. Then I'm forced to spam block the domain, which hurts the domains email reliability. I will change it as needed for testing purposes. So just use whatever you need to use to get the account created.