Different sport and different recruiting rules when S19 went through this, so ymmv.
It sounds like we did something similar, emailing Ivies and similar schools. S got varied responses ranging from radio silence to something similar to your email. A couple of the schools that appeared to have extra interest in the emails (like what you described) but didn’t contact his high school or club coaches were all over him on the first legal contact day, and he is headed to one of those schools in the fall. One that I thought was an athletic overreach when he first emailed them. Another that seemed really interested never did call him after the first legal contact day. But they recruited a couple stars for his position in the class ahead of him, which is why I think S went from being a highly sought recruit to being completely off of their radar.
I would definitely give them the info they are asking for. I would also periodically email updates to them, and to the other schools he is interested in.
It is difficult to predict who will ultimately be interested. As @Ohiodad51 pointed out, there is a pecking order. The top schools get their guys first, then the next tier, then the next, etc. So your S may move up on someone’s board, or can move down, depending on what happens above him. I had a friend’s son this year be told by a lower end D1 football program that he was the #5 linebacker on their list, and the 4 ahead of him were all guys they expected to go to P5 programs. But until those guys committed elsewhere he wouldn’t be offered a scholarship.
Early interest is also dependent a bit on recruiting budget and coach organization. S had a coach who had ignored all of his emails call and tell S out of the blue that S was one of their top priority prospects. This was 7 months into the legal contact period.