It seems like a pretty tall order, but I really want an open source access point controller daemon that knows how to provision and manage a wide variety of APs from different manufacturers.

So you'd have one services that can provision Ubiquity, MikroTik, TPLink and other APs and manage the clients.

Alternately, run OpenWRT on the APs themselves, and then you just need one provisioning protocol.

Does it support seamless roaming of clients between group of APs?

Last time I've tried, it was not supported by any open source solution.

Well AFAIK the core seamless roaming in Unifi is using hostapd, which is the same AP software you use on OpenWrt. See 802.11r Fast Transition.

I think it should even be possible to get seamless roaming between Unifi and OpenWrt with correct configuration of hostapd.

Now that would be interesting! Multi-vendor support is on the radar, but haven't started looking into it much yet.