I would mentally separate all his skills and take an inventory. Reading writing spelling math social skills speech general self confidence, self care, organization, independence… anything you can think is important for school. Are all of those skills one year or more advanced?
My kid is super advanced in certain subjects but also has lagging skills that need time to develop. So I never have asked for grade skip and school has not suggested it. I’ve asked for single subject advancement in elementary but they said one grade level bump doesn’t even do him any service because he’s several years advanced and there’s no prebuilt path to do that. (For example, you can’t take 6th grade math in 4th grade b/c 6th grade math is taught in another building. Also a super advanced 4th grade reader doesn't necessarily want to read what’s socially/emotionally appropriate for high schoolers.)
He will get math acceleration in middle school, but there’s a track to do that that’s prebuilt. with that, he’ll end up in college math classes mid high school. Skills wise that seems fine, but there’s a lot to manage logistically - different expectations, different location or online, managing 2 school systems simultaneously, exam timing, etc. That’s a lot to ask of a 16 yo that may or not be able to drive yet.
I would think about what’s available, and where that path ends. Taking college classes in high school? Graduating HS early? Starting college early? Finishing college early?
In my kid’s case we have opted to keep him with same age peers, use some gifted and acceleration options when available. Expand his learning outside of school. Going for breadth and depth rather than acceleration. He does get bored sometimes. But he also has some luxury with his free time to explore interests. We don’t have a very achievement or competitive mindset as a family, we lean more into exploring interests. And having a whole life. for example my kid has spent a lot of time baking. It’s not academic. It’s not achievement oriented. He just likes baking a cake to share with friends and family. He’ll probably use that to be a good home cook down the line. That’s as much of a win as advanced math if you’re asking me.
I would not only take an inventory but place it in the context of their likely advanced developmental level. There is a reason why ADHD assessments take into account IQ - significantly higher IQ leads to higher compensation of symptoms, or milder (or differently-presenting symptoms). Even if not all skills are 1 or more years advanced, one can still grade skip as long as they are not too bad, and academically 1+ year ahead. Though note such skill differences in organisation, self-care, as the developmental gap can indicate ADHD (though rule out other physical/mental disorders first). As my psychiatrist had keenly noted, even good attention (relative to age norms) is a deficit relative to a 98-99th% + IQ and thus is developmentally inappropriate compared to developmental level. I would also note any compensation strategies the kid has used to fix the weak areas (Pomodoro method, app blockers, etc.).
You can accelerate social development and compensate for hyperactivity/impulsivity and inattentiveness to a decent extent in various cases. This is why many ADHD teens are missed. If there are any big gaps, perhaps see a doctor or psychiatrist.
The Internet provides a huge range of maths content, as Eagle Mum explains. However, it is often significantly more difficult to self-study from the Internet than it is to learn with a competent teacher. For instance, not getting distracted by games, understanding the content/problem solving, etc.
If the stuff of logistics is too difficult, I would recommend graduating HS early and starting college early, or perhaps skipping a grade later. Taking some college classes in HS can be done concurrently - perhaps even AP/IB may allow skipping credits. As someone who used to quite like math but probably had ADHD that I compensated for to a decent extent at that age (getting away with little study/organisation, telling myself to study for a few minutes to ease myself into more studying) to the point few (Except my classmates) suspected ADHD... the self-care skills are good. However exploring interests should be limited to some extent... otherwise the kid may focus too much on interests.
But glad to hear you focus on the whole person! I follow that... just with some acceleration first (Grade skip) then work on the stuff, to save time.