one clock, 2 steppers can be 3 pins if you share the direction pin or
you can use 2 pins if you only ever move one direction and just set the dir pin.
the link shows that he put 4 on a board with drivers and one micro.
Then created a network for the 504 stepper version. with one micro as the orchestra conductor
there is a dual shaft, dual stepper similar to the one you linked, but stacked, not flat, X40 8798
seems to be used for clocks with 2 hands or instruments for cars and the like,
I know that there is a push to never use more than one micro for a project, but, in some cases it is easier and cheaper to have one board with one micro as a module for a larger project.
If I were to do this, I would make a PCB with one Micro, probably a MapleMini, then put the drivers on that board.
and just wire the steppers to the drivers. smaller footprint, the MapleMini is Arduino comparable for digital stuff like this and have 34 pins GPIO pins so despite it's quirks, 4 of them could run your project.
The ESP8266 could work and with a few shift registers, you could do many motors as well.
As a note, the open loop of running steppers will lead to offset errors over time.
manual setting of each motor should not be hard, but would be a pain in a piece of art.
You could put one IR sensor behind each face to detect a hand. Then spin the hour hand and zero it, move it, then zero the minute hand. then put them both to zero. It would take an additional pin per face.
for the project, I would offer to get a couple of each of the motor types and a bunch of A4988 stepper drivers under $1 in lots of 5 on aliexpress
then hook it all up and test it out.