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There is some conductive PLA material made by Protopasta, and here is a project where they made a little capacitive controller:
When you said keyboard, at first I thought you meant a computer keyboard, but something like that with hexagonal keys would also be cool. If you have a multi-material printer capability e.g. dual nozzle, toolchanger or filament changer, you could embed circuit traces into the body of the keyboard. That would probably add a lot of troubleshooting and complexity though and not everyone has multi-material printing capability.

Conductive traces could be printed onto a flat surface of a printed part though, with a simple material change. You could effectively print 2D traces onto the backside of the keyboard. The capacitive effect of the buttons may be hampered by long thin traces with high resistance though (or crosstalk between traces from capacitive coupling) so wires may be needed for each button. This would require some experimentation to see if it would work, but fully printed electrical traces would be cool just because. Then print the buttons separately in conductive material, and perhaps use a 3D printing pen with conductive filament to join the buttons to the electrical traces.

I don't know of any conductive filament that is transparent (since they contain conductive fillers like graphite), so any LED backlight would have to be in the body of the keyboard.

Not really sure on the electrical side of things, but there is a whole custom 3D printed mechanical (computer) keyboard which has a lot of overlap and could probably figure something out. Kinda like this:

Makey-Makey Game controller made with Proto-Pasta Conductive PLA