Shouldn’t the moon have… 24 time zones as well, depending where on the moon you currently are?

No, the moon’s rotation isn’t on a 24-hour cycle. I’m not a astronomer, but I pretty sure since it’s tidally locked to earth and on a 28-day cycle around the earth, a lunar day is actually 28 Earth days, but I’m not actually sure how that would factor into the number of time zones (but I’m pretty sure it would be more complicated than just 24 time zones to match 24 time zones on earth).

Plus, I think the speed of the moon relative to the sun is different enough from Earth that you need to take relativity into effect, which is the real headache here.

Pretty sure it’s both pointless and impossible to have an earth-like timezone system in an object that has coordinated rotation and translocation cycles. Meaning this mess we call “timezones” shouldn’t exist in the moon.