ZeroMQ Notifications in Browser JavaScript
If I understand this correctly, you're trying to communicate with Bitcoin Core through ZeroMQ directly from the browser.
This is not possible.

The reason why JSMQ only supports Websockets (ws://) is that browsers don't allow you to use raw TCP sockets. The only protocols you can access from within the browser are HTTP(S), Websockets, and WebRTC (which is still not supported everywhere).

In other words: the browser won't let you communicate directly through ZeroMQ.

If you don't want to rely on an external API, then you can always write your own and run it on the same server/computer where you are currently running Bitcoin Core.
This software should receive updates from the Bitcoin node through ZeroMQ, and send them to the browser via websockets.

As long as it supports websockets or HTTP(S) you'll be able to connect to it from within your browser.