I know how scary it can feel to let a timid/ somewhat daft cat outside. I had a ragdoll cat for years and we didn't let him out, on the advice of the breeder, as they are 'too stupid' and 'can't defend themselves'.
When we moved house, my ragdoll was about 6 years old, he'd spent his life indoors (occasionally out in the garden supervised like yours). He displayed behaviours very similar to what you are describing. We once had some other cats come in our garden who were quite territorial and he lacked all awareness of it, he was just rolling around on the floor! So obviously we thought, we can't let him roam free.
We then moved to a place with a larger garden, in a cul de sac that was a bit quieter. There were other cats around and the occasional car. I don't know what your living set up is like, but honestly, biting the bullet and letting him roam was the best thing we ever did.
He is so much happier and more content now. He actually rarely leaves the garden anyway, but it's made such a big difference in his behaviour and personality, he is like a different cat.
It was hard to do and of course we were worried something bad would happen. But it turned out that all of our worries about him 'needing to defend himself', getting lost, getting run over, were absolutely unfounded and we just needed to trust him.
Your cat is a British Blue, by the looks of the picture. I see them out and about near me all the time so there is no issue with your cat's breed that means they can't go out. I know she is timid and nervous, but that might be partly because she is indoors and living such a limited life. She is bored and frustrated and that is why she is so clingy.
If you are in a suitable place i.e. not directly on a busy main road, I really would suggest that you take a deep breath and try letting her out. I know it's hard, but it could be the best thing for her. Cats were not made to live in the confines of human houses.