For most networks, a proxy would be best done though dhcp option 252, which allows specifying a URL that contains a wpad configuration file, or through DNS.
However that's less annoucement and more making the service discoverable.
Any service can advertise itself using zeroconf but you’d need to establish a service type for proxy and have a client(browser) know to watch for it and connect through automatically (if approved by user)….
Depending on the environment you can often use wpad (windows proxy auto-discover) you have to be able to host a PAC file someplace and have a domain, but it fits for your use case.