You are speculating. You don't really know if they are a big supplier or not. Also, if miners "are a big supplier", then you would expect the price to be falling all the time as they continue to sell new bitcoins every day.
Because that's exactly how it works. Supply and demand. Google for it and you will understand. The mmore supply, the lower the price. That's science, not speculation.
Also do you expect all miners to be holders, or just suppliers of BTC to exchanges? They mine and sell most of them, because they need to pay energy costs.
There is no correlation. There was a steep rise in price a few months after the first halving, but not after the second halving (unless you include the rise that followed more than a year later. Furthermore, there have been several steep increases that do not coincide with any halving.