How does one share a single WebSocket connection across multiple browser tabs?

I'm aware of multiple questions/posts suggesting SharedWorker. However, it is not a viable solution due to the poor adoption of SharedWorker (only 35% globally according to Can I use at the time of writing), not to mention it has been dropped in Safari.

I have implemented a working version using SerivceWorker, which has some SharedWorker's capability, to share a single connection across tabs. Unfortunately during testing I realized that ServiceWorker can be killed/stopped by the browser, especially when the devtool is not opened. I'm also aware of some workaround to prevent this behaviour, such as pinging the ServiceWorker periodically. I would like to ask whether there is a proper way to handle this.