Sounds like fun and an excellent small set of steps and tasks for a beginning FSM project.
I recommend you avoid using any FSM library. I am biased to code I write, that’s where the fun is, so a grain of salt shoukd go with my observation that most libraries take more time to come to grips with and use than simply learning how to roll your own.
As always, YMMV. google
arduino traffic lights FSM
and poke around a bit for something to get your teeth into.
a7