The TLDR is: HarmonyOS is Huawei's mobile OS. The first few versions were based on Android, but version 5, also called "HarmonyOS Next", lacks native support for Android apps due to the use of a different kernel and other low level system bits being different. In their marketing Huawei pitches it as being built from the ground up, but of course some elements were borrowed from their Android spin. Currently, HarmonyOS is mainland China-exclusive, globally you get an OS based on Android 12.
As for the other Chinese OEMs, they all use a spin of Android. Xiaomi has HyperOS, Oppo has ColorOS, OnePlus has OxygenOS (nearly identical to ColorOS, and indeed, branded as such in mainland China), and Vivo has OriginOS (previously funtouchOS).