Most STM32 timers have four (or more) channels. A quadrature encoder requires two channels. Is it possible to use a single timer on an STM32 for TWO quad encoder counters? If not, can the other channels be used to generate PWMs for driving H-bridges?

No. Look at Figure 266 in STM32G4 Series RM0440 Reference manual. Only the first two timer channels are connected to the encoder interface (tim_ti1fp1, tim_ti2fp2).

and "Encoder interface mode acts simply as an external clock with direction selection. This means that the counter just counts continuously between 0 and the auto-reload value in the TIMx_ARR register (0 to ARR or ARR down to 0 depending on the direction)." . So, you cannot use the other channels for PWM.