Well, the tech to upgrade planet health is called Emergency Infrastructure, I believe Basically, planet health and population are not related at all.

When the planet is being bombed, the infrastructure gets damaged and population gets killed. Each bombing weapon actually has set values for how much population it kills and how much hp damage it does. As long as your planet has hp remaining, it will remain under your control, even if population drops to 0. Once the planet's hp drops to 0, the planet is lost.

In game terms, bombardment is not to kill off the entire planet's population, but to destroy the government infrastructure. So, think of increasing planet hp as building ground-based bunkers, shelters, etc that would make it more difficult to destroy your colony on it. If that helps The population lost is a secondary effect to bombardment, but it starts growing again after a certain amount of time has passed after bombardment.

Hope that answers your questions!