Is not getting an offer letter normal?

A recruiter landed me an interview with a company and she called me to say I got the job! In the call, I asked a few questions and asked if there was an official offer letter I could see and she said no, her company doesn’t typically do that for contract positions. She said she would take the time to write something up for me since I asked. She then made me verbally agree to the offer on the phone and we hung up soon after.

I emailed her to check-in as I didn’t think it would take too long and i was anxious to see something official. She emailed back saying that her computer broke. [Note: she also called me from her personal phone because something was wrong with it] She said she would try to get me a write-up soon for my records but it’ll have to be Monday since she’s out of office tomorrow and her computer is totally broken.

I can barely relax and enjoy the fact that I was offered the job because it doesn’t feel concrete. Is all of this normal? It feels fishy and I feel like something will slip through my fingers.

Do contracts not need offer letters? Is verbal agreement enough?