Although I don’t recommend running (addressable) LEDs using POE (If you want to anyway, take a look here) using POE can still be great to use as primary or standby for a Brainboard! The before linked article goes much deeper into using POE extractors but here are some recommendations if you wish to use POE for primary or standby power:
12v 2p pluggable
Using a 48v-52v to 12v POE extractor is by far the cheapest option available. These generally come with a barrel plug, you can use either one of those barrel-to-2p converters (Do not use for LEDs but for this purpose with max 500mA they are fine) and a little cable or snip off the barrel jack and then use the 2 wires that come out to input into the orange 2p pluggable connector on the brainboard (not a powerboard!).
*The voltage of the LEDs you are running does not matter, all powerboard inputs can vary in voltage without issue!
Another option is to use the USB-C input of the brainboard to supply 5v! These are a little bit more expensive then the 12v variant but also not too bad if you’d like to do it this way!
Isolated vs Non-Isolated
Looking at converters from POE to either wires or USB-C there are 2 types that are available, Isolated and Non-Isolated converters. Which one will work? Un-officially both but officially according to the POE guidelines when the device you are powering using POE can also be powered by a second power source (which is true in our case) the 48v -> 5v/12v needs to be done using an Isolated converter. The selection linked above are Isolated converters (as far as I know) but I felt it important for you know this little technical bit!