Most don’t. An exception was Netware 5 where DHCP database was in NDS and shared by the servers. Some fancy Enterprise systems might do similar.
Regarding conflicts DHCP servers should test that an address is free using ICMP or ARP (local only) and exclude the address as a conflict if it’s already in use.
Microsoft DHCP Server can do what you ask, i.e. replication and lease sharing. You can learn more here
With MT there’s a thing called authoritative dhcp and delay dhcp, so you can have “active-backup” dhcp with mikrotiks kinda easily, but syncing configs and static leases is up to you, also no guarantee backup server leases same IP to the client as primary did. DHCP standard says client may ask for the same IP as he used previously, but it’s up to server to admit it or just ignore and lease whatever is free.