I’m not aware of any other way to sync between them than HomeKit, and that requires you are an iOS user to build the automations. There’s a web UI plugin for HomeKit, but I don’t think it allows you to create HomeKit automations.
You also need either an Apple TV 4 or newer, an iPad that can run the latest iOS or a HomePod to run the HomeKit automations. There’s a project to build a stand-alone HomeKit server that is in the works, but it’s not that expensive to just buy a used Apple TV 4 and shove it in a closet with the other hubs and bridges if you don’t want to use it for anything else.
As far as getting the regular Mijia Hub running with HomeKit, there is a plugin for Homebridge, as long as your Gateway is v2. But I have no personal experience with it. I just have the Aqara HomeKit Gateway, which was just $40 USD. That for me was worthwhile to get an official HomeKit enabled gateway and not have to mess with a config.json file and potential incompatible devices, on top of having to build HomeKit automations.
I’m not suggesting this is an easy route if you’re not already in the Apple ecosystem, and yes you do lose battery indicators in HomeKit. The Aqara hub currently does not support them. No idea if that Miji Homebridge plug-in does or not. But that’s minor. I’m not sure they were even setup right when I had them paired to HE directly. I think I needed to adjust the voltage, because after a year they still read 100%, so that can’t be correct. I’m not a worrier about batteries. When the device stops working and I can’t repair the connection, then the battery is the next thing I’m going to check with a tester anyway. Maybe you get battery levels with the MiHome app, which can do HomeKit setup, but not as easily as the Aqara app. I’ve not used that app since I got the hub because even though there is a way to switch back and forth between the MiHome app and the Aqara app, I found doing so was causing me to have to setup all over again if I changed countries to see what was coming in the Aqara lineup (because China always gets the devices first, I like to peak at what might be coming ).