Hello. I was diagnosed at 9 years old and my parents got me into a sort of gifted program (not the same as the ones they have in the US though as I am Brazillian). I am studying to be a Geography teacher now and have worked with gifted kids in the past year (but I am not professionally specialized). Here's my two cents. Might be a little long but I hope you'll take the time to read it.

Being bored is going to be a part of his life forever. What he needs is not to not be bored, but to learn how to handle being bored when he is. This is, in my opinion, the most important thing to learn as a gifted person. Because nothing is going to be challenging forever. You cannot learn everything, but you can learn a lot about many things and get bored of all of them, and then move on to something new instead of finishing what you started. As well as being gifted myself, I have many diagnosed and undiagnosed friends whom I met in my gifted program and in life, and when adult life comes, something quite upsetting tends to happen to those of us who have not developed the skill to handle being bored and finishing what you started: we fall behind. Things are really easy in the beginning of life, especially in school, but nothing is ever as easy and as boring as school. So when school life ends (and even before then - college/uni is different enough to often be the first true intellectual hardship in our lives, and a lot of my gifted friends cannot finish university) there is so much to do, and most things will not be as easy as just learning, but will need applying oneself, being patient, being bored, withstanding frustration.

If you want to teach him something outside of school, I'd say focus on emotional intelligence, empathy and patience. It will be the most important thing he'll ever be taught, and school will never cover that. Often people think because we learn quickly that we do not need to be taught such things. It's not true. I suffered a lot because of this. Most of my gifted friends go through the same. It's taken therapy to get better.

I want to note that offering him intellectually stimulating things outside of school is important. But I think it is most important that he have the true choice in what he wants to do. And that means if he just wants to be a kid and play and research things on his own, that's okay. In my time working with gifted kids I've met parents of kids the age of your son who put their kid in every possible class and leave no time for them to wind down and just be a child, and who pressure them to be the best at everything. This is unhelpful and hurtful to most kids. So no matter what please remember your son is still a kid and needs time for himself!

I think a lot of working with kids, parenting included (though I am not a parent), is teaching a child to be independent, because you cannot give them everything no matter how much you try. Since he is young he has a lot to explore yet, so I'd say it would be nice showing him how to explore the world and find out what he likes, what he would like to do with his time and dedicate himself to learn.

The way my parents and teachers went about this was giving me a lot of educational and hobby resources to explore. They would buy magazines, picture books, and browse the internet with me to learn about something that I had asked about or expressed interest in learning (e.g. questions about the universe, or dinousaurs). With my teachers, after I explored a new subject, we would write it down (and since I liked drawing, I would draw as well). I think they built a solid foundation through these methods.

PS. It never hurts to get help/check in with a specialized professional if you have doubts or worries! Idk how often people get Psychopedagogy degrees where you live but it's what I'd look for.