PSE 2023 Organizer.

The People room has two tabs - Named and UnNamed.  Once a person's face stack has been identified and named in the UnNamed tab, the stack is moved to the Named tab and their recognized face icon will appear under their name there.  Depending on the number of files in your catalog (and the specs of your computer) it can take quite a while for the program to anyalyze the photos and place the identified faces into the UnNamed stacks.  Also note the Hide Small Stacks check box.  If this is checked, you will not see any recognized face stacks with less than four (?) faces.  So, you may want to uncheck it to see all of the faces that have been recognized.  Of course, if faces are recognized and added to the small stacks, they then move to the UnNamed grid whether the box is checked or not.

I can't explain why you only see faces after clicking on the Places tab other than possibly your computer may be taking a while to load the faces.  Also, if you switch from People to Places and back again, I believe you will return to whichever People tab you were using when you made the switch.

Yes, if you own a prior version of Elements, you get a prior user discount (usually about 20%).  Only you can tell whether it is worth you upgrading to Elements 2024.  The big new features of Elements 2024 are the option to have a dark or light UI and auto-synching your photos with the Cloud.  You can download a free trial of Elements 2024 and see if the new features are worth it for you.  A full comparison between versions 2023 and 2024 can be found here.