How about going through all the research, available tests/tools and resources that many of us (older, self-identified people who were missed in childhood due to the clinical landscape at the time) have done? Then, if you and he think that he's likely autistic, you can decide together whether or not a formal diagnosis is worth pursuing.
He's 15, that's well old enough to understand this stuff and decide for himself if he wants a formal diagnosis.
I will caution that it's very difficult to get a diagnosis as an adult, so his age is an advantage here - "I'll do it later if it becomes necessary then" may not be a possibility, until things improve to the point that adult diagnosis becomes easier/reliable.
Official diagnosis will open doors for him to supports that he may need as he gets older. He may be managing well now, but as the pressures of life change and increase (for instance, he goes to college, or into the workforce) they may exceed his ability to cope and he could require support that he doesn't currently. If he does, that official diagnosis will be critical for him to access that support and those resources.
I'm in favor of getting an official diagnosis while it's possible and relatively easy to obtain. However at 15, even knowing that he is likely autistic, engaging with the autistic community and having that community support (where he can learn coping skills, skills to manage sensory issues, etc.) will put him leaps and bounds ahead of where many of us were at his age (I didn't really figure any of this out until I was in my late 20s and didn't understand most of it until I was in my 30s.)
You don't need an official diagnosis to take advantage of the community resources (information, online groups such as this one, articles) that are freely available. If you and he decide not to pursue the official diagnosis though, he may regret it later, which is something to consider. There could also be drawbacks to having that diagnosis (depending on where you live and what his career aspirations are - I don't want to attempt to get into it because every situation is different and there may be no drawbacks for him.)
It's all important to consider and he's really, really lucky to be in a position where he gets to consider it all. Many of us weren't. Kudos to you for doing the absolute best that you can (I wish more parents would reach out to the autistic community instead of blindly accepting what they're told by schools/psychologists!)