Electronic – Digital circuit to toggle on rising edge of two signals

Even a PLL isn't going to preserve the waveform (including duty cycle) of its reference input, unless you add a second circuit to it to specifically do that. For example, the PLL could drive a one-shot whose pulse width is controlled by a feedback loop that compares the output duty cycle with the input duty cycle.

The best way to do this in an all-digital manner is to have one circuit that measures the frequency and duty cycle of the input signal (if those are the only two parameters you care about), and have another circuit that synthesizes a new signal with the same duty cycle and the desired frequency based on those measured values. (I have done something like this myself when building FPGAs that need to do frame rate doubling/halving on video signals.)

The output signal will in most cases be an approximation of the signal you actually want, and you'll have to decide how good that approximation needs to be.

You are right. Edge triggering is just a much narrower form of level triggering, and depends on timing. Inside an edge-triggered device, the changing clock edge is just turned into a pulse which causes it to accept the inputs: a level trigger! But the level trigger is very short. It must be so short that the outputs are not able to propagate back to the input to do any harm in the time that the edge-triggered pulse appears and disappears.

Edge triggering would not work if signals propagated instantly through wires and had unlimited slew rates.

Also note that clocks can be divided into phases to solve problems where this isn't fast enough.

A master-slave flip-flop is an example of clock phasing. It splits the clock signal into two phases by reacting to both rising edges and falling edges, but differently. Input is accepted on a rising edge into an input latch, and then on a falling edge propagated into a second latch where it produces output.