Why would people invest loads of money in BTC after the halving and not before?
People choose to invest in the BTC market post-halving due to a reduction in its supply, which will increase demand, and you know that when supply becomes low and people demand anything high, it increases price pressure.
...when halving is happening Bitcoin supply is cut into half, meaning that the scarcity will make price to increase.
It's simple demand and supply. There's always demand for Bitcoin so when the supply reduced (in this case just the circulating supply and not total supply) it'll make the price to go up and that's why the halving increase the price.
Those are repeating a very common misconception.
First, the supply is not reduced by the halving. Instead, the
increase in the supply is reduced. The supply increases with every block until it reaches 21 million.
Second, reducing the supply does not increase the demand. In general, supply and demand are independent functions.