When pressing F11 to toggle in and out of full-screen, it does not save options.txt, so upon the next launch of Minecraft the previous fullscreen state is restored, not the one that was set.

Code analysis

Mojang mappings 1.20.1 - KeyboardHandler.java

if (this.minecraft.options.keyFullscreen.matches(key, scancode)) {
    this.minecraft.getWindow().toggleFullScreen();
    this.minecraft.options.fullscreen().set(this.minecraft.getWindow().isFullscreen());
    return;
} 

here we can see the code that toggles fullscreen doesn't trigger Options#save.

I have implemented this fix inside my mod, Debugify, so people who find this particularly annoying can use my mod to fix this among other bugs as well.