Most of my devices are running Tasmota, and Tasmota needs to know the address of the broker.
But that is all moot now. Thanks to the tip from Paul-Reed, I can now force the broker to be on the same IP on the new router.
Besides that, I also determined that Tasmota works just fine with the brokers hostname instead of the IP address. So as I casually (no rush now) flash new versions of Tasmota on them, I will use the hostname of the broker instead of the IP address.