Can logic analyser show high impedance state?
I have seen older logic analysers that were capable of showing if an input signal was in a disallowed state.  That is: the input voltage was in the region between a defined logic LO level and a defined logic HI level.

This was many years ago and I don't recall which logic analyser it was - I'm guessing Tektronix but I honestly don't remember.

Certainly the little logic analyser I use today (Open Bench Logic Sniffer from Dangerous Prototypes / Seeed Studio) does NOT have that capability.

Do note that even if the logic analyser DOES have that capability, something has to make the input signal go into that disallowed state when the signal is in the high-impedance state.  That may require you to add external voltage dividers to each of the inputs to drag the signals into that disallowed state when high-impedance.