I commuted 81 miles one way work for 12 years. The traffic worsened a great deal over that time. For the past few years especially. The hospital enacted a new time and attendance policy which was too strict. (one infraction even for being one minute late
You could not h ave over 12 infractions per year because that was automatic termination.
I was at my limit for time and attendance when my car broke down and I had no transportation to work. I called to notify the supervisor of my problem. She said
That would put my time and attendance over which was an automatic termination.
So, I assumed I was fired. A few months later I received a separation notice
Stating I quit without notice. Will I be eligible for unemployment benefits?

My facility has a similar policy. We are allowed a 2 minute grace period 9 times a year. This gives us 18 minutes a year to be late or we are terminated. However, there are exceptions to the rule, unless there is an open and obvious zero tolerance policy. Your mistake was assuming you were terminated. Had you gone to HR to plead your case, there may have been a different outcome. Yes, your supervisor notified you of the policy, but there is a chain of command as you well know.

Considering your commute I am relatively certain that HR would have made concessions for you. In the end, you should have reported to HR before assuming you were automatically terminated. Unfortunately you most likely will not get unemployment. You may have to appeal if you are denied.