The solution I found is that I was able to configure the password recovery feature while logged in under my TP-Link account.

I ended up using a gmail account for the recovery since my outlook email account did not work.  I used Claude AI to work me through the process because the instructions on the TP-Link site were next to useless and did not really explain the process.  Setting up the authentication password in gmail is not a straightforward process if you are not familiar with setting up app passwords.

Interestingly enough a Google search said it was not possible to change a router admin password or set up password recovery using a TP-Link account without the local password for security reasons.  This makes sense but clearly is not the case.  While I was not able to change the router admin password while logged in with the TP-Link user account (because the admin password had been reset and I didn't know what it was), I was able to set the recovery and simply change the password through the recovery page.  I simply reset the password back to what it was.  

This is pretty buggy software and it would have been much faster to have simply reset the router and re-enter my preferences but I managed to do all this without disconnecting the internet while my wife was watching TV in the other room.  So there's that.