I've got one of the CC2531 Router stick. It was recongnized as "device" It seems to work well, but it is so verbose that I suspect I've got a 500 error after a couple of days due to that attitude.
Here following an example of the logs of few hundreths of second ...
i've used at least two different firmware loads. One was supplied from an older distribution of zigbee2mqtt, other is the one linked here. I believe both report every 60 seconds. The link also has debug versions which I have not tried. I viewed the 60 second report as a positive since my time is important and limited while setting up the network. The stock CC2531 firmware is only a sniffer not a router.
It seems to have paired directly to RP02-IACOPO? Mine all began paired to the controller. A few of them ended up not on the Neighbor Table but I always try to change that. CC2531 radio is kind of polarized and rotation of the device often helps out quite a bit.
This isn't a "normal" device. It will all depend on the firmware. If you want normal, use something off the compatible devices list. Otherwise, you may not get normal functionality.