I'm pretty much mirroring most of what's best said here. The thing about Millennials and Generation Z'ers is that the now homebody social atmosphere of being online or on your phones 24/7 has bred more introverts than extroverts these days. At least, it's made their extroverted intuitions and thinking very suppressed which can probably cause someone who isn't introverted to be more depressed and not understanding why. Or someone who is introverted, more fearful or drained too quickly from outside stimuli and that they don't belong simply because they are often misunderstood or deemed uninspiring/lazy by older generations. Simply for lacking the confidence and experience of being outside and not absorbing enough of it as second nature as the earlier generations. The social groups/circles have grown significantly smaller too so seeing one that they never been around before will most definitely make them uncomfortable and even give social anxiety to someone whom necessarily never had it before.
There's this overwhelming feeling of teenagers these days with some Generation X or Baby Boomer parents that nothing they do is good enough or they aren't good enough. They lack confidence greatly and end up closing themselves off than actual rebelling like the previous generations because there is less heart to heart and understanding as most indications of wanting to share themselves is seen wrongly and/or judged. Not saying this is you, I can see you're not like that at all. I apologize, I'm just rambling now to get to my point that relates to this lol.
In my opinion, A rebelling teenager is actually actively fighting their depression or distracting themselves from it the best they can and more times than not are actually extroverted.
Similar to what's been said here already, just support them and their decisions and have heart to hearts just as often or not more than pushing/scolding. They just may be late bloomers or need that reality shove to get things going over time. And positive criticism from the world rather than family that they may feel don't understand them. Let them fall into their own dirt and pick themselves up, you're just there to help pick them up if they struggle getting up is all.
Your son might actually be perfectly fine and content with his bond with you. You might actually be his best friend. I'm biased here because that's how I was as a kid. My father was my best friend.
Personally, it sounds like your son is more mature for his age group and just doesn't feel like he fits in with kids his age or might actually feel like a outcast rather than being bullied. Being self-aware that you don't belong and will be seen wrongly can actually keep him from wanting to meet new people. Or, he might be a introverted feeling type that gets mentally drained fast around too many new people so he avoids it all together. And his negativity could be his view of the world and that everything done is in vain paired alongside his generation's already thoughts and feelings of they aren't good enough or constantly misunderstood.
For what it's worth, you seem like an amazing and most definitely a very caring Father, especially with how much he's on your mind and how much you talk about your children. Any child would be extremely lucky to have you as a father.