Thanks so much for the reply.
I interviewed for the position in a mid-size city public school system working in the administration building. There was one interview on Zoom with a team of potential colleagues. A week or two later, I had a telephone interview with the team. The next day, my potential boss verbally offered me the job. I went into the office to see the space to do a final check on the job environment. It's a fine office. I asked some questions about the HR part and she said, she doesn't handle that part of things and sent me info on who to contact in HR. Last Friday, when I agreed to the job and gave a start date, new boss said she forwarded this on to HR as I asked for a written job offer before I give my quit notice to my current job. It's a few days later and no offer has come forward. New boss checked in and I said, I'll have to delay starting until the letter arrives. Nothing yet.
It's a municipal job and I understand about their bureaucracy structure, but is there more to the story? I am so glad I did not talk to my current boss about this potential. The job has a good salary for me and offers security. I guess it's wait and see?