Cool little game! Reminds me a lot of Papers Please. Looks really great too.
I personally found that trying to solve each ship as fast as possible felt pretty fun, maybe that could be incorporated more directly into the gameplay/scoring somehow? I know there's already a global timer and scoring system, but what if you get a bonus for correctly handling a ship within a certain time limit?
I want to point out some minor technical stuff (that didn't factor into the rating), the game wouldn't work due to misaligned UI until I made my browser window the same size as the game window. In the future, you can go into the project settings of the game, find the setting called 'stretch mode' and set it to either canvas item or viewport. Doing that will scale the game with the screen automatically. Viewport keeps the resolution, canvas item sets it to the screen resolution (there's probably more differences, but I can't remember them off the top of my head). Also, it may be better to use all control nodes for the interactive parts (rather than the current system which I'm presuming combines sprite2Ds with invisible buttons). Godot's buttons can have icons, which can replace the sprite2Ds, you can use a texturerect for the wooden panel and a combination of control nodes and various container nodes to get the spacing you want.