mDNS, SSDP and maybe CoAP and LLMNR send with a hop count so that these datagrams are not being routed. That is why you need a repeater daemon on the router or fiddle with the hop count via firewall rules to be able to route these datagrams across VLANS.
I can confirm that you can effectively distribute these protocols across VLANs in practice. This needs a repeater software and appropriate firewall rules (SOLVED: SONOS across multiple VLANS).
There is nothing that the Unifi switches can do for you with that regard. There are L2 features regarding IGMP, but mDNS and SSDP are designed for local use over multicast and do not need IGMP.