Be sure that you have also enough Zigbee Router devices. I highly recommend read and follow → Zigbee networks: how to guide for avoiding interference and optimize for getting better range + coverage
That is, it is not enough to make sure that the Zigbee Coordinator is avoiding electromagnetic field (EMF/EMI/RMI). You also need to add many mains-powered devices that act as Zigbee Routers (which are most but not all mains-powered devices), or for best possible experience add a few dedicated Zigbee Router devices.
Not sure if the use the same chip part number (model) but they both use radio chips from the same radio chip series (Silabs EFR32MG21) so the difference is the application firmware. Home Assistant SkyConnect uses the standard Silicon Labs EmberZNet application firmware with EZSP (EmberZNet Serial Protocol) interface. ConBee III uses its own deconz application firmware (which has its own deconz serial protocol interface).
What might be different otherwise is the circuit board design and components uses (including the antenna design and whether or not to have additional electromagnetic shielding cover protecting the extra sensitive components for the antenna). Note that the Home Assistant SkyConnect board does not have any electromagnetic shielding cover and uses a PCB antenna design so it is extremely sensitive, (on top of the fact that all Zigbee radios are very sensitive to EMF because they are low-power and low-bandwidth radios).