I don't think the stability in Bitcoin's market is a sign of confidence, but more so a sign of complete neutrality. Bulls don't have much to be bullish about, bears have not much left to be bearish about with how strongly supported the base bottom is. In other words, it currently makes perfect sense for the price to remain stable.
As it is right now the stock market might seem to be in an early state of correcting, but the danger here is that right now the general public is expecting it to tank further, and this is usually a bullish signal for smart money to buy the dip. I'm 50/50 on the stock market correction. It wouldn't surprise me if it does end up tanking further, but it doesn't surprise me either if it reaches a new all time high in the next 6 or so months. I'm not going to burn myself on that.
Well, since like you said, the bulls do not have the momentum to get the market up and the bears seems they have been completely tapped out with no more strength to even be able to break the $6k support, should we then say, with the stock market experiencing correction, there could be a possibility to see smart moneys, trying to move into a market that has been oversold. I am just thinking right now though, based on the way most investors usually think in most cases. I actually believe the stock market will most definitely tank further and still has a lot of room to go down, but in the meantime, I would not be surprised if we get to see a push up in the crypto space. All the same, just assuming things
.