This is forseen as to help lower the supply of bitcoin into market which lead to increase of scarcity.
...the market demands increases as the supply decreases
The halving does not lower the supply of bitcoins. The supply of bitcoins increases every block until there are 21 million bitcoins. At no point does the supply go down.
...if there is a bakery with some special cake, people rushed with the mentality that these cakes will be finished soon because the supply is limited..
That is a bad analogy because bitcoins are not consumed.
Which means the production cost of each Bitcoin increases. Ideally, this is enough to increase the price of Bitcoin.
The price of a bitcoin does not depend on production costs. In fact, it is exactly the other way around. Due to how mining works, the production cost tends to approach the price. In other words, the production cost depends on the price.
Because no miners will be selling their Bitcoins at a loss.
Why do people always say that miners will never sell at a loss? That is absurd. A miner must pay for their operating costs by selling their bitcoins regardless of whether the price is higher or lower.