Instead of "I want you to also know that I have taken this time to deeply reflect, and I have learned from my mistakes. In the future I can ensure you that all journeys will be covered by a valid ticket and that this will never happen again."
Why don't you just say:
"I have learned from this mistake and in future I will make sure that I always have a valid ticket for my journey"
Bear in mind that they are only charging you for one incident. You haven't said if you have done this previously (and you don't need to say here) and so keep everything in the singular. "Mistakes" sounds like you have done it before and might make them dig deeper. They might do this anyway, especially if you bought tickets online.
Chatgpt is awful for these things. It is overly wordy and overblown. Where you have written it yourself, such as the phrase " I am early on in my career and would not like to mess up any prospects by one stupid decision." Then it actually reads ok.
Post your own version here and we will give you more feedback.