I would almost always prefer to make a dhcp reservation for devices in your router, to make sure they always get/have the same IP.
Do you have a mesh network with several nodes or are you really refering to routers or repeaters? Those are different devices and mesh nodes are (most of the time) superior over repeaters. Especially when the are mutual connected by a lan cable. Then it shouldn’t differ to which node a device is connected.
Routers are different device types (which could be part of a mesh network), but I don’t think you refer to those.
If you are really using repeaters; then see if you can’t replace them by mesh nodes, preferably connected by an lan cable.
You might want to consider a different wifi network for your smarthome devices. Of course routed to you other network vlans.
And alway connect by lan cable where possible.
Make sure your wifi channel(s) are not interfering with tour Zigbee channels, if you are using Zigbee.
See: here and here.
Fritz sometimes calls a repeater connected to a Fritzbox router also a mesh repeater.
But when it creates a separate wifi network (evt with the same name) it not a real mesh network.
There is quite a lot to explain when it comes to networking to explain here. You’d have to Google for that…
Also try a Fritz forum/community to get some information, as it exceeds smarthome networking.
If you start by giving us the Fritz modelnumbers, we might be able to tell you what network you probably have.