Imagine a FPGA that has one shift register with latch instantiated in the firmware, that outputs its state to the LEDs onboard, and reports back buttons state. On the other side is atmega8 with firmware that drives the FPGA and controls its LEDs, and read buttons from it.

It works. You can grab Verilog code and reuse it to make your FPGA talk to your atmega8 and vice versa.

My flow is verilog file -> yosys -> arachne-pnr -> icepack -> flashrom tool on raspberry pi -> olimex evaluation board. On the atmega side flow is ASM file -> avra -> avrdude on raspberry pi.
And, yes, I can control mouse and keyboard using those buttons as long as programming socket is connected.