Windows 11, Outlook, Office 2021
Overall Question: How to put names and emails into the contact group named Politics? Any group for that matter.

Edit: Answered. See the first answer and my reply. Thank you.

Actions: The group has been created. In outlook, click on Address Book
The list of names is presented, the group Politics is there, bolded as compared to regular names.
Left click on Politics. Nothing. Right click, New Entry. Pops the dialog New Entry
At the bottom is the text: Put this entry in Contact (This computer only) - <an email name>
No, not there. Click the down arrow. The only options are
<same email address>
Contacts (This computer only)
NO, the new address is to go into Politics.

Question 1: How can I fix that and/or work around.

Try it anyway with Contacts selected
Go back to the mail email dialog to select a different address.
NO These dialogs to add a new contact are Modal. I must close three levels of dialog, find the new address, copy with ctl-C, then open three levels of dialog again.

Question 2: How can this be done without opening and close all three dialogs for each and every address to be added.

Action: go back to the top dialog for Address Book, the one that shows the contacts and contact groups. Click and drag a selected contact into the new group.
NO! That will not work. Click and drag just selects multiple contacts.

Question 3: What are the steps to move a contact from the top level of the list down into a contact group?

New question: Button Submit New Thread did not work. In the tag field typed office. It list numerous versions from about 2003 to 2013 but nothing later. Selected that, but as noted at the top it is version 2021.