I can work with this!

I came here to say almost exactly what you did.

Nah, the F is displayed while counting down the time of an active exercise period, while C is displayed when counting down the time of a resting period

I wish I had your research skills. Where does it even say that?

The letters may have been chosen for early, limited 7-segment display drivers, such as a hex-to-7seg decoder. However, these fell out of use when transistors were no longer expensive in the 1990s and it made more sense to minimize the number of chips rather than each chip’s complexity, so the main microcontroller used 14 GPIO pins or a single external LED driver to multiplex all 6 digits. Before the 1990s, it probably did not make sense to make this device digital at all, I think gyms would just use analog clocks with marked dials.