There are keyboard matrices that can accommodate more keys with fewer pins. E.g. https://kbd.news/Square-or-round-robin-matrix-1400.html. This one can do 12 keys with 4 pins. But needs some careful component choices to avoid ghosting.

HDMI cables, with 19pins (I will use it in my next build), or flat cables, which you can find in different sizes and pin counts (I used some with 10 pins in my Rommana). Both types of connector and cables can be easily found in Aliexpress.

I’m not too familiar, but I’ve been told shift registers or IO expanders can save pins. In my small amount of research, it seems like they work (both of them seem to do the same thing? I’m honestly not sure what the difference is) by converting parallel signals to serial signals like SPI or I2C. For example, with I2C (the one that requires fewer wires), I think you could wire up your 4 columns… to the 4 wires of the I2C standard, which are VCC, ground, and two data lines, but if you’re able to use those same lines for ground and VCC for the rest of your board too, you’d be effectively saving two wires. Note1: If they share VCC cable with the RGB’s you’d have no ability to cut the external power, but maybe for a wired board you don’t care about that. Note2: Not sure if you could wire all 7 matrix wires to one expander… for me at least that wasn’t an option because to not have to do constant polling, you can only use an expander on the output side of the matrix. Avoiding constant polling is a power concern when building a wireless board.