Almost all programs use both 32bit and 64bit integers, sometimes even smaller ones, if possible. Being memory efficient is critical for performance, as L1 caches are still very small.

Garbage collection is a feature of programming languages, not an OS. Almost all native linux software is written in systems programming languages like C, Rust or C++, none of which have a garbage collector.

Swap is used the same way on both linux and windows, but kicking toolbar items out of ram is not actually a thing. It needs to be drawn to the screen every frame, so it (or a pixel buffer for the entire toolbar) will kick around in VRAM at the very least. A transfer from disk to VRAM can take hundreds of milliseconds, which would limit you to like 5 fps, no one retransfers images like that every frame.

Also your icon is 1.1Mbit not 1.1MB

I have a gentoo install that uses 50MB of ram for everything including its GUI. A webbrowser will still eat up gigabytes of ram, the OS has literally no say in this.