gnome-terminal works perfectly in normal mode, but once it enters fullscreen mode, there is always an empty bar at the bottom (see gif below). Is it possible to remove that?
Terminal emulators work with a grid of cells: a whole number of cells both horizontally and vertically. That's why when you resize the window by dragging its corner, it resizes in unusually large steps rather than pixels. (KDE's terminal emulator "konsole" is a notable exception which you can resize to any pixel size, and you'll see the same empty bar at the bottom and right as you do in gnome-terminal's fullscreen mode, even when konsole is not fullscreen.)
In fullscreen mode, gnome-terminal is forced to a size that's not a multiple of the size of its character cells. Utilities and applications running inside terminals have no notion of such partial cells and couldn't draw in the remaining area, it just doesn't exist for them.
You might want to experiment with different font sizes, you might find one where an integer number of cells just fit (or at least the gap is not that large) – but it'll probably break as you open your second tab and the tab bar appears.