Is It Appropriate To Write A Thank You Note To A Prosecutor And Judge After They Were Exceptionally Kind And Considerate To Me In Traffic Court?

I want to express my gratitude but I’m not sure if this is done or inappropriate in any way. I am thinking of asking the court administrator for guidance , but I am not sure if that is appropriate either. I have the court administrator’s email from a recent interaction. Is the below e-mail okay, or should I avoid doing this altogether?

Dear (her name),

I hope this message finds you well. Following our recent email communication, I wanted to kindly seek your guidance on a matter.

I recently had a court appearance where both the judge and the prosecutor were exceptionally kind and understanding. I am deeply grateful for their consideration and would like to express my thanks.

Would it be appropriate for me to send a thank-you note to both the judge and the prosecutor? If so, could you please advise me on the most suitable course of action, such as sending a written letter to the court, an email, or if there's another preferred method? Your assistance in this matter would be greatly appreciated.

Thank you very much for your time and consideration.