The cloud controller is a (surprisingly heavyweight) service that manages a network of unifi devices. It can run on a raspberry pi, or an x86 container / vm.
If I wanted to run it all the time, I’d try putting it in a docker container on my synology.
Instead, I have an sd card for my raspberry pi that has nothing but the controller installed. The main downsides to this are that it is easy to lose the sd card, and that the controller gathers bandwidth/usage/wifi connection reliability stats, but only when it is running. I don’t get those unless I boot up the RPi to diagnose some network issue (this has never been an issue in practice).
One advantage of the RPi setup over a synology container is that it has both a ethernet jack and a wifi adaptor. This is surprisingly helpful when bootstrapping complicated mesh topologies.
I have a UDMpro which self-hosts a controller, thou personally if i knew it couldn't be joined to another controller i'd have gotten something else so i could throw it in docker (which runs on a NUC with the storage off a synology)