Do modern systems - say within the past 10 years - still operate in this way when a PS/2 keyboard is plugged in (yes, some motherboards still do have PS/2 ports, bizarrely)? Or have modern CPU architectures, microcode, and updates to the x86 instruction set removed it?
Does it still work this way when you plug a USB keyboard into a PS/2 port via an adapter (I'd imagine yes, but I don't actually know)
PS/2 still works the same as it always has. No changes there. It's not really possible to change how PS/2 operates because it wouldn't be backwards compatible with old keyboards or software.
Legacy stuff sticks around for a while and generally doesn't change, since it needs to retain backwards compatibility. Modern x86 processors also still have a "real mode" with 1MB RAM max, like what the 286 versions of DOS and Windows 3.0 used to use.
You can buy industrial PCs and motherboards today that not only have a PS/2 port, but also other legacy stuff like parallel and serial ports, ISA slots, etc. There's actually motherboards that have ISA, PCI, and PCIe all on the same board. There's 25+ year old machinery that's still in use and extremely expensive to replace, so it's not uncommon to have new computers with legacy connectors/ports in industrial environments.
Enthusiast motherboards still have the ps/2 ports as well. Usually because the usb controller is the first thing to stop working when the bclk gets too high or you're going sub 0 cooling.
Apparently some enthusiasts still use PS/2 keyboards because they have slightly faster response times / lower latency, and better support for n-key rollover.
The absolute lowest level of computers haven't changed much, we still fuck around with interrupts. However, USB peripherals are a LOT more complicated than this, and if I'm not mistaken they're polled by the connection master