OK. Carefully deleting the PVC did cure the random IP problem. It did not, however, cure the login problem. I've copied the awx-admin-secret and used it with the ID "admin", I've changed the secret and used that, and I've changed it back. After each change, I get this:
10.58.22.1 - - [28/Dec/2022:17:00:35 +0000] "GET /api/login/ HTTP/1.1" 200 6240 "
https://it-network-engineering-awx.apps.os-dev-nadc.mycompany.com/" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/
108.0.0.0 Safari/537.36 Edg/108.0.1462.54" "10.96.107.239"
[pid: 37|app: 0|req: 6/15] 10.58.22.1 () {80 vars in 2284 bytes} [Wed Dec 28 17:00:35 2022] GET /api/login/ => generated 5714 bytes in 39 msecs (HTTP/1.1 200) 10 headers in 492 bytes (1 switches on core 0)
2022-12-28 17:00:35,940 WARNING [0001a06cbf444c49804afa67b2ee5fbe] awx.api.generics Login failed for user admin from 10.58.22.1
2022-12-28 17:00:35,946 WARNING [0001a06cbf444c49804afa67b2ee5fbe] django.request Unauthorized: /api/login/
2022-12-28 17:00:35,946 WARNING [0001a06cbf444c49804afa67b2ee5fbe] django.request Unauthorized: /api/login/
[pid: 35|app: 0|req: 6/16] 10.58.22.1 () {86 vars in 2474 bytes} [Wed Dec 28 17:00:35 2022] POST /api/login/ => generated 5920 bytes in 221 msecs (HTTP/1.1 401) 10 headers in 502 bytes (1 switches on core 0)
10.58.22.1 - - [28/Dec/2022:17:00:35 +0000] "POST /api/login/ HTTP/1.1" 401 6445 "
https://it-network-engineering-awx.apps.os-dev-nadc.mycompany.com/" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/
108.0.0.0 Safari/537.36 Edg/108.0.1462.54" "10.96.107.239"
Again, the fresh install I did works just fine. The admin password works. So, it seems this is some sort of artifact of my failed and deleted project of the same name from 2 days ago. What might I have created then that is persisting across 3 deletions?