Default digital/analog pin state - input or output? (do unused pins need to be grounded to prevent floating inputs)

I think so, but it's probably ignored because most likely it won't cause any problems.
I don't like it, so I won't leave it as INPUT.
Because the GPIO of the AVR is internally connected to the CMOS buffer/Schmitt trigger for digital input.

EDIT:
Excerpt from the ATmega328P datasheet, the pads connected from the pins are connected to the schmitt-trigger input via the transmission gate.
(The transmission gate does disconnect the digital input circuit from the pad (and schmitt-triger input are tied to gnd) when uC goes into deep-sleep mode.)

If you make floating the input at bare schmitt-trigger IC will probably got warned in this forum.
But mysterious, no one says anything even if the schmitt-trigger input is floating "in the microcontroller".
I feel a double standard for this at forum.:expressionless: