I believe that in the case of Bitcoin, the velocity should be calculated using the quantity of coins that are apparently available and released for use. I believe this because Bitcoin means a variety of things to different people and organisation, and its capabilities are fairly complex.
There seems to be a decent number of ways to consider the matter, Jet Cash. Of course, if we are talking about effect of the actual physical coins, then we are talking about more of a hard effect rather than the soft effects of expectations, so I personally believe that it could be presented either way, and sometimes physical alone can be considered and sometimes expectations of future issuance and whether bitcoin is actually on schedule regarding issuance (which seems pretty concretely set when it comes to bitcoin).
Of course, bitcoin is amongst the first of asset classes that is being attempted to be used as money and to have a solid scarcity. Sometimes, I was taking issue with some of the stock to flow discussions because from my reading, sometimes I was missing the parallel that was being attempted, so they were trying to suggest that bitcoin is mined and new coins come into existence, and sure there is some truth to that, but we also know what that is going be with a decently high level of certainty, even accounting for the various scenarios in which consensus could be changed to inflate the BTC supply.
Many of us have also noticed another phenomenon and that is before bitcoin halvenings there is all kinds of pressures to attempt to keep BTC prices down, and even to spread FUD suggesting that bitcoin halvenings were going to cause the opposite effect than what logic would dictate, including the dumbass death spiraling of mining power based on loss of incentives to mine. Anyhow, what seems to happen is the various powers that be in the bearwhale space push the BTC price down for as long as they can and as low as they can. And it seems to me that part of the reason that we end up having such an explosion in the price that ends up happening a decent amount of time after the halvening is because the actual physical supply of BTC ends up being so constrained that there has to be a kind of physical resolution that does not even matter so much about what people think about the future, but then the explosion will cause a kind of piling on, too. So the physical and the psychological will surely play off of one another, even when sometimes one or another might seem to be more of a driving factor under certain circumstances that are trying to be described or explained.