From my experience, the Kemper does not act as a DCHP server. It sends discovery packets at startup and will use an external server if found (e.g. your AP). If no server responds it falls back to the so-called "link-local" network range.
You're referring to an APIPA address, right? That makes sense.
That also tells me my setup is not going to work. I got a TPLink PoE switch so I wouldn't have to use a PoE injector. Also got the PoE powered MicroTik maP, which has a super small footprint. Unfortunately, the maP only works in router or Bridge mode. In Bridge mode the DHCP server is disabled and in router mode the communication between the wireless and wired networks is NATed.
On my Android tablet it looks like the app is using broadcasts to discover the Kemper, so that's not going to work across a router/NAT, and in bridge mode my tablet won't get an IP address, which means I'd have to enter an APIPA address manually every time. Also, the power brick for the TPLink is at least as big (if not bigger) as the switch.
(listing all this info in case someone else is researching/trying the same thing).
I saw your setup on the thread Syntek mentioned. What PoE injector is that? Looks like it has a pretty small footprint. And are the power supplies for the GL.iNet and the PoE injector the black and yellow bricks right above above the PoE?