How can I make iTerm2 hotkey window fill out the whole screen? I am using MacOS Catalina, and I use iTerm as my terminal. My problem is, that every time iTerm has been closed, and opened again, it only opens in half screen. I know I can drag it down to full screen with my cursor, but it's super annoying if I have to do that every time I open it.

Is there a way to make it full screen by default?
Yes, go to preferences under the iTerm menu item. When the panel opens, select the Profiles option at the top of the panel. Once that opens, click on the Hotkey Window option, and then click the window tab near the top right. In that window you can define the window size or on the right select instead of Normal, Full Screen. See the image below.