Zigbee2MQTT how to get Connector/Router a device is connected to?

The requirement will be unique to each enviroment and specific devices uses. Some buildings have small rooms with dense wall/cealings/floor that kill Zigbee as its signals are low-power and the messages are very short (small frames). Then some Zigbee devices will have much worse antennas and antenna design than others, as well as have weaker Zigbee radios than others. So two similar setups can get very different results depending on which home they are installed and where exactly the devices are located.

But a the general rule can still be said to be; when in doubt, add more Zigbee Router devices. However, buying and adding a few great Zigbee Router devices will have a much greater impact compared to many poor Zigbee Router devices, so that is therefor what I recommend.

Again, strongly recommend follow the tips I collected here → Zigbee networks: how to guide for avoiding interference and optimize for getting better range + coverage