Read the last paragraph if you want a simpler solution.
The current (May 2020) controller interface doesn't give you a clear ability to reserve
IP addresses for wireless access points. Instead it gives you the option of statically
entering all of the information. You can use the customization features of
config.gateway.json to do what the GUI does not let you do.
To figure out your network name, you'll probably want to ssh into your USG and then get
your shared-network-name by running the following command: mca-ctrl -t dump-cfg.
Once you have a network name and its associated subnet, you can enter in the static
mapping(s) you desire for your AP's MAC address(es).
A UniFi Controller running on MacOS will store this file at the following location:
$HOME/Library/Application Support/UniFi/data/sites/default/. You can find your
unifi_base value with help from this article.
The simplest solution is to skip trying to configure your device directly. Copy your AP's main MAC address (not the one used by WiFi clients) and then add that MAC address on the clients page, and remember to check the "Fixed IP" box and enter in your desired address.