I want to learn how to sing despite me being bad at it. I love to sing, it frees me and brings me joy! I recently got a voice teacher. I know this is a probably a dumb question. (Probably because I’m anxious and don’t believe in myself) Will I improve my singing and eventually become a pretty decent sounding singer with a vocal teacher and persistent practice?
As long as you avoid damage to your voice (which is one reason why a teacher is a good idea) it is clear that you will improve with guidance and practice. And unless you have a damaged or malformed vocal apparatus there is nothing that should hinder you to develop your voice. Learning to sing is equally about developing muscles, technique, body feeling and getting rid of bad habits carried over from speaking. As such you being a ”bad singer“ does only mean that you are not there yet. But this can quickly change once you start to train your voice.
Finally as you said singing can be a very freeing and empowering thing, it can help you get rid of stress and bad feelings, so if you enjoy it you will have a benefit even if you do not become the greatest singer of all time. Singing in a choir can be lots of fun and socially rewarding. You do not need to be flawless to justify making singing a part of your life.
It's certainly worth a try! Also, you could sing alongside other, better singers - join a choir or other performing group. And just do a lot of singing!
Don't be discouraged if you can't copy the performance of your favourite singer, in their key. They had to pick the right key for THEM. So do you.
Usual disclaimer about practising so hard that it hurts.