How does an output switching from HI or LO to HI-Z affect an input in CMOS?
The Hi-Z output and thus the inverter input will reach a voltage level which will depend on several factors. The node will have a very high impedance to ground so any noise/charge/leakage currents it picks up can affect the voltage.

If there is a clock line running nearby and that line is capacitively coupling to the node, the inverter could pick up that signal and give a clock at the output.

Without much external disturbances like clocks and noise, the leakage currents from the NMOS and PMOS transistors in the tri-state buffer will work against eachother. If for example the PMOS transistors leak slightly more than the NMOS transistors then chances are the Hi-Z node will go up in voltage and eventually reach the supply voltage. But at a different temperature or same model chip but from a different manufacturer or even same model from the same manufacturer but from a different batch of chips the opposite could also happen (NMOS leaking more I mean). This is unpredictable so we want to avoid that always !

Anyway, it is bad practice to leave a CMOS gate input floating like that. So you'd never find this situation in a properly designed circuit. What most circuit designers do is define the voltage in Hi-Z mode by using a pull down or pull up resistor.

In TTL a Hi-Z is usually interpreted as 1 (one). But again, this is bad practice and it is better design practice to define all inputs properly just like in CMOS logic.