It is correct, battery-powered devices don’t act as “Zigbee Router” devices (a.k.a. repeaters/extenders).
There are already several other long threads in this forum that specifically discusses range extending Zigbee so you might want to look at this for tips on specific “Zigbee Router” devices. See example:
- https://community.home-assistant.io/t/advice-on-zigbee-range-extending/175882/
- https://community.home-assistant.io/t/zigbee-range-and-how-to-improve/474130/
I too can personally recommend IKEA Trådfri Signal Repeater as a product because that is very good and inexpensive enough so you can buy more of them. Suggest that you start by buying three of them.
https://www.google.com/search?q=ikea+tr%C3%A5dfri+signal+repeater
Alternatively buy a few of ITead Sonoff Zigbee 3.0 USB dongles and flash ith Zigbee Router firmware as then you can use them in USB-changer for power to get the best performance for the money you spend:
- https://community.home-assistant.io/t/itead-s-sonoff-zigbee-3-0-usb-dongle-plus-v2-model-zbdongle-e-based-on-silicon-labs-efr32mg21-20dbm-radio-mcu-now-sold-for-19-99/442695
- https://community.home-assistant.io/t/iteads-sonoff-zigbee-3-0-usb-dongle-plus-model-zbdongle-p-based-on-texas-instruments-cc2652p-20dbm-radio-mcu-now-sold-for-19-99/340705
General advice for a stable Zigbee network mesh is that it is better to have many good “Zigbee Router” devices than it is to only have a couple of great ones, so for the same money, it will be much better to go with three or four IKEA Trådfri Signal Repeater devices than going with just one or two of any other Zigbee Router device for the same or less total cost of the investment.
Regardless, highly recommend reading and following these guidelines before buying anything specific: