Halving equals more scarce.
Halving equals less inflation.... it in no shape or form equals Bitcoin to be more scarce than it already. Scarcity in Bitcoin doesn't always play much of a role because during a bear market there are more sellers than buyers
It is not just about scarcity alone
As it is always about utility too as these two characteristics of an asset, service or good are complementary and work hand in hand. What I mean to say is that utility has the same effect on price as scarcity. If Bitcoin becomes more useful (when, for example, people start to use it more widely as a means of payment) its utility rises which leads to higher prices even if its scarcity doesn't change or even decreases (i.e. Bitcoin becomes more abundant). Conversely, if people become less interested in it, Bitcoin's utility goes down - along with its price