My brother thinks he is ready to move back into a place of his own. Any advice?

You are not responsible for him.

You are also not responsible for bailing him out of his choices in the future.

I know that we do feel responsible for someone when we have nursed them back to health and we want them to continue to take care of themselves, but we can't make them and we can't tear ourselves apart over their bad choices. So love him and let him decide what he will do and you decide what you will do.

He is an adult.
He has not been declared incompetent.
You can do noting but be there for him and support his decisions, you can guide him, you can give your opinion but that is about it.

This is such a very sad situation. Indeed, you honestly have no say in the matter with your brother being mentally competent to make his own decisions. I think you know where you started from, and I would bet that you have a pretty good inkling where it will all go from here. If you have sat him down and reasoned with him and he is still making this decision I don't see what you can do about it at all, but suffer when you see things beginning to go south. I would express your love, and your concern, and then tell him that you have no power to prevent him taking the actions he is taking. I am so sorry you are faced with this. I recently lost my brother. In the last year he entered Assisted Living when really he SO wanted to return to his beautiful little home. And he constantly told me that while it wasn't the choice he wished he could make, he recognized it was the one he HAD to make because of his poor balance and his early probable Lewy's diagnosis. He was so reasonable. He made the best of it all, was so exceptionally brave and stalwart. It pained me what he had to do, but the pain would have been so much worse if I had to worry about his safety. My heart goes out to you, and I hope for the best.

If he is of sound mind then he’s free to make his own decisions including where he lives and how he spends his money. Would his doctor say he’s competent?

Maybe, when u can, have him re-evaluated by his doctor and see if he feels brother is ready to live on his own.